Saturday, September 28, 2013

Government Provided Money Supply

I recently made a comment on to the effect that there should be a formula linking bank deposits, bank loans and money supply.  No one took up the challenge to offer a formula so an unfilled need remains.  This blog post will offer a linking formula.

The mere thought of a formula including money supply is, at first thought, ridiculous. Money supply is defined in many ways such as moneyness, convertibility, source, and backing.  A formula is realistic only if definitions are tight and verifiable. At the end, any definition of money supply will be accepted only if it rings true with supporting data.

We will begin by thinking of money supply as a government provided product supplied in two interchangeable forms:  Federal Reserve Notes and Federal Debt.

Federal Reserve Notes are a dynamic product and constitute the usual way of transferring money in the United States.  Ignoring currency, all Federal Reserve Notes (held by the public) reside in banks as bank deposits.  We will assume that the total of all bank deposits is the total money supply formed by Federal Reserve Notes.

Federal Debt is a static money product but freely exchangeable with Federal Reserve Notes.  Federal Debt usually includes a time delay.  Federal Debt is formed when Federal Reserve Notes are issued.  Additional Federal Debt is formed when privately held Federal Reserve Notes are exchanged for Federal Debt.

Government Provided Money Supply (GpMS) is the sum of Bank Deposits (BD) and Government Debt (GD).

1.  GpMS = BD + GD

Bank Deposits, all denominated in FRN, are dynamic in the extreme.  On any given day, massive exchanges between Federal Debt and Federal Reserve Notes occur resulting in an increase or decrease in bank deposit levels.  Accounting for this exchange is complicated by bank lending which results in an increase in deposits for every new loan and a decrease for every loan payment.  At any one time, it is impossible to know which bank deposits are the result of earned savings, private loans, Federal Government loans, or Federal Reserve purchase of assets.

While we may not know the source of deposits, we can learn how much money is loaned by banks.  If we know that part of the deposits is from loans, we can assume that the remainder of deposits is from other sources which we will label as Legacy Money Supply (LMS).  We can then write another equation: Bank Deposits (BD) equals Total  Bank Loans (TBL) plus Legacy Money Supply (LMS), or

2.  BD = TBL + LMS

Equations 1 and 2 can be combined by substitution to give

3.  GpMS = GD + BD = GD + TBL + LMS.

Equation 3 fulfills our goal of linking bank deposits, bank loans and money supply.

The success of any formula or theory depends upon the ability to explain or predict events.  Next, we will see some graphs comparing GpMS and M2.

In all the graphs, we will use Federal Reserve data.  Bank deposits will be series DPSACBW027SBOG which is deposits in all commercial banks.  Federal Government debt will be series FDHBPIN which is Federal Debt held by the public.

The Federal Reserve also holds Federal Debt but all these holdings are represented by FRN in the hands of either government or public holders. This condition results in FRN counted as part of DPSACBW027SBOG, or, FRN resting in Federal Government accounts, not commercial bank accounts.

We will use the Federal Reserve product M2 for money supply comparisons, and GDP for additional comparison.

The data series chosen may not be the best for accurate measurement of the concepts so these data choices remain under review.

We see from Figure 1. that GpMS is always larger than M2.

Figure 1. GpMS compared to M2.
Figure 2. is the annual change of GpMS compared to annual change of M2.  It is interesting to notice that the trend lines between about 1990 and 2000 are reversed.  GpMS trends down and M2 trends up.  That difference may be worthy of future discussion.

Figure 2.  Annual money supply change as measured by GpMS and M2 

Next we look at annual money supply change as a percent of total in Figure 3. This shows a dramatic reversal of trend in year 1995 for M2.  A similar reversal for GpMS does not occur until year 2001.

Figure 3.  Annual Change of GpMS and M2 expressed as a percent.

Our forth graph will show LMS.  LMS is identified as Legacy Money Supply but it could also be considered as a measure of backing for bank loans. We will use the Federal Reserve series TOTLL to measure bank loans.  Figure 4 indicates that backing for bank loans actually became negative prior to both the 2002 and 2007 recessions.
Figure 4.  Variable LMS.  This variable could be considered as backing for bank loans.
The final graph is a comparison of velocity measured as GDP divided by money supply.  Figure 5. The breaks in GpMS and M2 trend lines are distinctly different, as are the slopes.

Figure. 5.  Money Supply Velocity found from GpMS and M2.

The Government Provided Money Supply graphs compared to M2 graphs show many differences.  These differences can be expected to be the subject of future post on this blog.

Monday, September 9, 2013

Federal Debt and Bank Expansion of the Money Supply

It is widely accepted that Fractional Reserve Banking allows bank loans based on deposits.   Considering banks as a whole, any loan creates a new deposit without reducing the deposit of any other customer.  The lending bank creates a new asset (a contract to repay) and assumes a new liability (an obligation to restore full value of money to all depositors) in exchange for making this loan and deposit available.

Once expanded by a loan, an increase in available deposits remains in the system as an expanded money supply until the loan is repaid.

If there were no limits to this process, the increased value of all deposits could be used as justification for increased loans.  A new loan would equal a new deposit automatically so would there be no need for deposits to precede loans.  Loans and deposits could be created simultaneously.  This is prevented with limits.

In the United States, the Federal Reserve legally requires banks to hold reserves, currently 10% of all demand deposits.  This effectively limits loans to 90% of deposits and creates a limit to deposit expansion.  A 10% reserve allows a theoretical expansion of ten times the original deposit.

If the discussion stopped here, we would expect bank loans to be about 10 times reported deposits but data available from the Federal Reserves indicates that the ratio is dramatically less than an average of 1:1.  What is going on?
Figure 1.  Ratio of bank loans to deposits is unexpectedly less than 1:1 on an average.
The logic of money supply expansion has one important precondition: The borrowed money must be available to be loaned again.  This precondition is fulfilled theoretically by assuming that the loan-based-deposit is spent into the system and then continues to exist someplace as an account entry until the loan is repaid.  The single bank equivalent is a loan which once spent, comes back to the bank in a closed system, such as a bank on an isolated island.  In both cases, the loan-based-deposit could be used as a base a second, then third time, and so on. The precondition is considered completed.

This precondition may not be met in the United States Economy.  Follow the path of a loan-based-deposit as it is spent.  Until it gets into the hands of savers, it moves very quickly through the hands of the private economy and government, moving from bank to bank.. Fast moving money is extremely risky for use as a monetary base.  A bank would certainly not want to lend money based on a deposit that might only reside in the bank for one day!  The large number of banks in the United States acts like a divider of the whole-bank concept, negating the expansion precondition of stable availability.  Only the initial expansion is certain, and this is an expansion of two (a doubling), not ten.

As previously mentioned,  even a doubling is more expansion than is indicated by Federal Reserved Data. The data suggests that loans are nearly always much less than deposits, barely exceeding a 1:1 ratio just prior to recessions.  Does this suggest that the system is operated without limits?  No, there is another path that accounts for the less than 1:1 ratio.

The Federal Government has run a deficit for most of the last 50 years.  Most of the deficit is funded with money borrowed from the private economy. Government borrows (first) the excess expansion from bank loans and then, if more is needed, from itself acting through the Federal Reserve. Finally, Government purchases from the private economy, thereby providing money for future loans.

The result can be tracked using Federal Reserve Data.  About half the expanded money supply is held in banks as deposits.  The second half is held in the form of Federal Debt (Note 1.) which is near money and accepted at face value for purposes of complying with Reserve Requirements.   Figure 2 shows the sum of bank deposits added to Federal Debt, which will be about double loans at banks, on the long term average.

Figure 2.  When Federal Debt held by the public is added to bank deposits, the relationship to bank loans is about 2:1 on the average.  This relationship builds the case for considering Federal Debt as part of money supply.
This post will conclude by pointing out that bank loans result in deposits.  Each bank loan has an original deposit that preceded the loan so we could expect to locate two deposits for each loan.  Surprisingly, the expected result of two deposits to one loan is not observable in Federal Reserve Data.  The deposits not-accounted-for have been loaned to the Federal Government and can be found accounted as Federal Debt.

Being debt of government and very safe assets, these missing deposits in the form of Federal Debt can legally be counted as bank reserves. These missing deposits in the form of Federal Debt could also be counted as part of the national money supply.

Note 1.  The label "Federal Debt" is used generically but a more precise definition would be "Federal Debt held by the public".  Federal Debt as a trust fund obligation is not counted.  Federal Debt held by the public, as defined in this post, is accounted by the Federal Reserve as data series FDHBPIN.


Sunday, September 1, 2013

The Widow's Cruse and Derivative Loans

Many bloggers are currently writing about the widow's cruse and the relationship of bank loans to money supply.  My latest tack is to consider the changes that would occur if an economy moved from a limited-bank economy to an economy with banks as we know them.

In this model, the initial economy has a completely fiat currency with no derivative loans allowed.  Here I define derivative loans as "loans from an institution that result in at least two parties having claim on the same underlying asset".

The initial economy can have banks but all loans are single party loans.  That is, all loans are clearly tied between lender and borrower, with lender well aware that borrower is spending the lenders money.  Any expansion of the money supply under this system must come from the sponsor of the fiat money supply.

The total amount of money in circulation can be measured by the difference between total amount issued less the amount borrowed back by the sponsor as the sponsor strives to maintain value of a fiat currency.  This difference should be slightly less than the amount on deposit at institutions because some portion would be held in wallets and under mattresses.

Now we will change the model to allow derivative loans (DL) by banks.  In this modified model, loans can be based on the deposits in the bank.  Money sitting in bank storage, similar to sitting under a mattress, can be put to use and  can stimulate an economy.

DL loans have three very important properties:

(1)  When the loaned money is spent, it will result in increased deposits owned by third parties.  The third parties are unlikely to deposit at the bank making the DL loan, but are likely to deposit at banks acting within the fiat money system.  The result can be measured initially from an increase in bank deposits by the amount of the loan (again excepting part held in wallets and under mattresses).

(2)  It is impossible to distinguish between Original Currency (OC) and DL.  This creates a situation of increasing DL based deposits.  This process has no upper limit.  Ever more owners can claim ever increasing deposits in accounts.

(3)  Transfers between banks are limited to transfers of OC.  This is an extremely important limitation.  Assume that a deposit holder writes a check and the check is deposited to another bank.  The second bank does not automatically credit to the bearer's deposit account.  Instead, the second bank issues a draw against the currency assets of the bank of check origin.  Two conditions must then be satisfied:

(3a) The check deposit owner must have funds adequate to cover the check.

(3b)  The bank must have currency adequate to cover the check.  This currency must be currency originally issued by government (OC), not a DL deposit.

The effect of properties 2 and 3b create a banking dilemma:   Ever more depositors have ever increasing claims on a fixed amount of OC!  Unchecked, this dilemma will end with collapse of the banking system when it becomes obvious that the system can not satisfy the the claims of all depositors with OC.

Returning to the blog question of widow's cruse,  it would seem that property 2 grants that generosity, the banks have a widows's cruse.  Unfortunately, property 3b would indicate that no cruse at all could ever exist between banks.

If these properties are correct, then important effects on money supply measurement necessarily follow:

A.  Original Currency issued by the government is the only money supply available. This can be measured as the difference between government expenses and government receipts.  Continuous deficits act to continuously increase the money supply.

B.  Original Currency exists like a "hot potato".  It does not disappear from public use unless removed by government, principally by running a budget surplus as when taxes exceed expenses.  Government borrowing does not  extinguish the OC, it merely puts it back into motion.  Measurement of OC by adding the deposits of all banks should closely match the amount of government debt held by the public. Differences between deposits and debt held by the public should be principally due to central bank efforts to control currency value.

C.  The sum of all outstanding loans has no bearing on money supply measurement. On the other hand, the sum of all outstanding loans is a vital measurement of the need by the public for future currency for loan payments.  Currency tied up in the hands of deposit holders is no guaranty that currency will be available to borrowers for loan payments.

D.  The change in bank loans is a measurement of money put into motion where it can be expected to increase GDP.  If government is repeatedly running a deficit, an increase in loans may increase tax income, thus lowering the needed level of borrowing to meet a preset budget.  This effect resulted in a rare government budget surplus in the late 1990's.  This same effect created a need for massive government borrowing beginning in about 2007 when loan failures forced massive government borrowing to maintain then existing government spending.

My conclusion is that the widow's cruse does exist like a rainbow does exist. Unfortunately, the widow's cruse only continues while conditions are correct, then it vanishes.