# The Money Multiplier — A Rite of Passage for the Wrong Reason

The last time I taught college-level Money and Banking, over five years ago, the textbook I was  coerced into assigning (but didn’t use) still had a section on the mechanics of how the banking system in a fractional-reserve regime could expand deposits (a component of “money”) by some multiple of cash reserves provided by the central bank. The Federal Reserve Bank of Chicago, one of my former employers, had published a booklet, Modern Money Mechanics, that explained how this process played out. When I was at the Chicago Fed, this was one of the Bank’s “bestsellers”.  In my undergraduate Money and Banking class, there were several questions on the final exam that pertained to the mechanics of this seemingly “magical” deposit-expansion process. I would be willing to wager that to this day, there still are questions on most Money and Banking final exams related to the mechanical process of deposit expansion in the banking system. It is a Money and Banking class rite of passage. Although the money multiplier is a convenient pedagogical tool, I suspect that the underlying economic significance of it is neglected in most classrooms. And that underlying economic significance is that the banking system in a fractional-reserve regime can, along with the central bank, create credit figuratively out of thin air. All kinds of credit, thin-air or not, enable their recipients to increase their current spending on something. But only thin-air credit unambiguously does not require anyone else to simultaneously decrease his/her current spending. Thus, a net increase in the supply of thin-air credit carries the strong presumption that there will be a net increase in total spending in the economy.

Now, for those of you who took a Money and Banking class, let’s review the essence of the money multiplier. For those of you who have not taken the class, let’s catch up. Suppose that there are n separate banks in the banking system, where n is a very large number. Now suppose that the central bank purchases \$100 of securities from State Pension Fund that banks at Bank 1. State Pension Fund’s deposits at Bank 1 have increased by \$100. Bank 1’s reserve account at the central bank has increased by \$100. MegaCorp, who is financing some new capital equipment to be purchased from CoreCapGoods sells some new bonds in an amount of \$100 to State Pension Fund. MegaCorp and CoreCapGoods both, coincidentally, bank at Bank 1.  Let’s stop here to consider what has happened to thin-air credit. The central bank purchased \$100 of securities from State Pension Fund, paying for these securities with funds created out of thin air. State Pension Fund then used these thin-air funds to purchase \$100 of new bonds issued by MegaCorp to finance its new capital equipment purchase. \$100 of new thin-air credit has been created by the central bank. Bank 1’s deposits increased by a net \$100, owned first by State Pension Fund, then transferred to MegaCorp and then transferred to CoreCapGoods.

Back to the money multiplier. Assume that by law, banks are required to hold as cash reserves at the central bank an amount equal to 10% of the deposits on their books. Further assume for simplicity’s sake, that banks earn no interest on their cash reserves held at the central bank. So, Bank 1 has an additional \$100 of cash reserves at the central bank, but because its deposits went up by only \$100, Bank 1 is required to hold only \$10 more of reserves at the central bank. Bank 1 has an additional \$90 of reserves at the central bank that are in excess of what it is required to hold and earn no interest. Now assume that Local Auto Dealer comes into Bank 1 in hopes of getting a loan for \$90 to finance its inventory. Because Bank 1 has the capital to support new loans and the loan terms are attractive to both parties, Local Auto Dealer gets its loan, promptly writing a check payable on its account at Bank 1 to Detroit Motor Vehicles, which banks at Bank 2. The issuance of the \$90 loan by Bank 1 increases thin-air credit by an additional \$90. In total, thin-air credit has increased a net \$190 up at this point.

Bank 2 now finds its deposits up by \$90 and its reserves at the central bank up by \$90. But Bank 2 is required to hold only an additional \$9 of reserves at the central bank (10% of the \$90 in new deposits), so Bank 2 has \$81 dollars in reserves in excess of what it is required to hold at the central bank. It just so happens that VentureCap walks into Bank 2 seeking a loan for \$81 to fund the start-up of AppNoOneNeeds. Bank 2 has the capital to support new loans and the loan terms are agreeable to both parties, so VentureCap gets its loan of \$81.The issuance of the \$81 loan by Bank 2 increases thin-air credit by an additional \$81. In total, thin-air credit has increased a net \$271 at this point.

AppNoOneNeeds deposits its \$81 in start-up funds at its bank, Bank 3. With those \$81 in deposits, Bank 3 also receives \$81 in reserves at the central bank, of which, it only is required to hold \$8.10 (10% of \$81). And so on. At the limit of n banks, the initial \$100 of reserves created by the central bank in its purchase of securities from State Pension Fund, will have been “multiplied” into \$1,000 of new deposits in the banking system(\$100/10%), \$900 of thin-air credit created by the banking system and \$100 of thin-air credit created by the central bank (or a net increase in total thin-air credit of \$1,000).

There are all kinds of real-world complications that can reduce or increase the size of the deposit and thin-air credit multiplier – complications upon which Money and Banking final exam questions are famous. Recipients of deposits may not want to redeposit the entire amount, preferring to hold a portion as folding money, i.e., currency. An increase in currency held by the public is a drain on bank cash reserves that lowers the value of the multiplier. In real life in the U.S., only checkable bank deposits are subject to reserve requirements. So, if an entity receives a deposit from some other entity and chooses to hold the funds as a deposit not subject to reserve requirements, the magnitude of the deposit/thin-air-credit multiplier will be increased. Even when banks are not paid any interest on reserves held at the central bank above and beyond what they are required to hold, some banks still desire to hold some “excess” reserves. To the degree that more excess reserves are desired, the magnitude of the deposit/thin-air-credit multiplier will be reduced.

More importantly, in the real world, banks do not behave according to this mechanical deposit/credit multiplier process although the end result of their behavior may be approximated by it. Banks don’t sit around waiting for deposits and reserves to come to them if they have good lending prospects. If a bank is approached for a loan it wishes to make, it does not tell the prospective borrower to come back tomorrow when it might have more funds to lend. Rather, the bank funds the loan by purchasing the necessary funds in some interbank market. Moreover, if banks are constrained by capital adequacy, which they were in the last financial crisis, they cannot support new loan growth even if they have a surfeit of central bank reserves. And, because banks’ required reserves are based on their deposit levels in some previous week, the deposit/bank-credit multiplier is not at all constrained by required reserves in the current week (right, Bob Laurent?).

But I digress. The point I am trying to make is that many Money and Banking professors spend too much time teaching their students the mechanics of the bank-deposit/bank-credit multiplier and not enough time explaining to them the important economic implication of the result of that multiplier – the banking system’s ability to create credit figuratively out of thin air.

To illustrate the economic significance of thin-air credit vs. all other credit, consider Charts 1 and 2. Plotted in both charts are the year-over-year percent changes in nominal Gross Domestic Purchases (Gross Domestic Product + Imports – Exports) from Q2:1953 through Q2:2007. Plotted in Chart 1 are the year-over-year percent changes in the sum of U.S. depository institution (commercial banks, S&Ls and credit unions) credit and Fed credit from Q1:1953 through Q1:2007. This credit sum is a variation of the thin-air credit to which I have referred. Thin-air credit growth has been advanced by one quarter to illustrate the effect of its growth this quarter on Gross Domestic Purchases growth nextquarter. The correlation coefficient between thin-air credit growth advanced one quarter vs. Gross Domestic Purchases growth during this period is 0.61 out of a maximum possible 1.00. Plotted in Chart 2 are year-over-year percent changes in total U.S. credit outstandingexcluding thin-air credit. This credit aggregate also is advanced by one quarter. The correlation coefficient between non-thin-air credit growth advanced one quarter vs. Gross Domestic Purchases growth is 0.29, less than half that of the correlation with thin-air credit growth.

So, here is my plea to Money and Banking professors. Spend less time teaching the mechanics of the deposit/bank-credit multiplier. Rather, spend more time explaining how this process creates credit figuratively out of thin air and why thin-air credit creation has such an important effect on the business cycle. Who knows? Perhaps one of your students will become a Fed official and can then explain this concept to her Fed colleagues.

Paul L. Kasriel
Econtrarian, LLC
Legacy Private Trust Co. of Neenah, WI
econtrarian@gmail.com
http://www.the-econtrarian.blogspot.com

1-920-818-0236

Source: The Econtrarian

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