The Money Multiplier

Update: Please read comments, as I often learn that I am still learning.

Update 2: see here.

I have received more than one kind and gentle email due to my post entitled “Austrian View of Fractional Reserve Banking: Tamny Mostly Right, Shedlock Mostly Wrong.”  The emails raise an objection to the following from that post:

Tamny: To Austrians, fractional banking leads to “excess credit creation” through what they refer to as a “money multiplier.”

The problem is that the very notion of a “money multiplier” is a logical impossibility; one that dies of its illogic rather quickly if analyzed in the lightest of ways. To explain what isn’t, banks are generally required to keep a 10% deposit cushion. Simplified, if a bank is the recipient of a $1,000 deposit, it can generally only lend out $900, or 90% of its deposits. What might surprise some is that the previously described loan is what has many Austrians up in arms.

To which I wrote in that post:

Please read the preceding again.  $1000 doesn’t become $10,000.  In fact, on prudently calculated reserves, $1000 doesn’t become more than $1000 in any economically meaningful sense.  The bank is confident in lending out $900 because it believes the depositor will not demand more than $100 from his deposit. (Emphasis added.)

It is interesting: the two individuals – the initial depositor and the subsequent borrower – hold two accounts totaling $1900.  But digits on paper aren’t excess credit creation in any economically meaningful sense of the term. (Emphasis added.)

I will preface my comments with the following: First, fractional reserve banking as practiced today is not fraud.  Second, markets are perfectly capable to regulate excess leverage at financial institutions.  I will not expand on either of these here as I have written on each topic more times than I can count.  These are not the primary purpose of this post; I only introduce these to clarify the baseline from where I will begin my analysis.

Given these two points (not fraud, markets capable of regulating leverage ratios), I lose interest quickly on the topic of proper banking / money / credit / currency issues.  If the market is capable of handling the issue, anything more I might write about it suggests central planning – one reason it strikes me that advocates of a 100% gold-backed standard are central planning.

As I do not think much further about the topic, it behooves me to consider that my statement in the earlier post might not be well thought through – as suggested by the emails.  The emails I have received come from multiple individuals whom I consider quite well versed on such matters; therefore it seems to me prudent to see if my statement holds water.

With that, let’s begin:

• Depositor A deposits $1000 at Bank A.
• Bank A, having previously calculated a prudent reserve ratio, determines it can lend $900 of these funds to Borrower 1.
• Borrower 1 now acting as Depositor 1, deposits $900 in Bank B.
• Bank B, again calculating prudently, loans $810 to Borrower 2.
• Borrower 2 now acting as Depositor 2, deposits $810 in Bank C.
• Prudent Bank C loans $729 to Borrower 3.
• Borrower 3, as Depositor 3, deposits $729 in Bank D.

And so on….

You get the idea.

There are four depositors in my example; in total, they have deposited $3439 – far more than the initial $1000 deposit.  They each hold account statements that, when summed together – equal $3439.  If I continue the example, the sum of the account statement totals would be $10,000 – no surprise.  As best as I understand Rothbard and those who point to this fact – a fact I do not dispute – this is the crux of the issue.

Now, why do I emphasize “prudent” reserve ratios?  Simply to not muddy the example with poor business judgment on the part of bank management.  Poor judgment by an entrepreneur might be cause for insolvency, but not a cause to ban the practice (do we really want to initiate force to ban what some might consider an imprudent business arrangement?).

So, in my example, prudent bank reserve ratio means Depositor A never draws more than $100 from his balance – he draws some, he adds some – but overall it fluctuates around the $1000 initially noted on his account statement.  Same for Depositors 1, 2, & 3 with their respective balances.

So, Depositor A never draws more than $100; Depositor 1 never draws more than $90; Depositor 2 never more than $81.  My example ends there, but if extended all the way to Depositor N (100 is more than enough), exactly $1000 is drawn in total by all 100 depositors at any one time – the same $1000 initially deposited.

Now, I admit the example is simple – each bank likely has hundreds or thousands of depositors – all that matters is the prudence of the aggregate ratio (and with larger numbers, the risk of error would seem to be reduced); individual banks on a day-to-day basis will likely move above or below the target ratio (after all, the withdrawal from one bank often gets deposited into a different bank) – but, if prudently calculated, this is why there is some reserve (in my example, 10%) to offset this risk.  Adjustments can be made over time if the overage or underage persists.

So, the math is correct, as depicted by Rothbard.  But the implications are incorrect: not all $10,000 can be spent at the same time – only $1000 can. 

“But,” you exclaim, “what if more than $1000 is demanded at once?”

It is beyond the purpose of this post to answer this question in any detail, but I offer a hint: other than cash withdrawals (a tiny fraction of the modern economy), every withdrawal in one place is a simultaneous deposit in another – therefore, privately-agreed-upon interbank transfer agreements will mitigate this risk; if this proves insufficient for any individual, grossly imprudent bank – bankruptcy.  In either case, the problem will be resolved and assets will transfer to entities as decided by contract and bankruptcy court.  But to avoid diving too far down the path of another issue, suffice it to say that I see no Austrian or libertarian reason to insert monopoly force in order to mitigate the risk of poor entrepreneurial judgment.

In summary, there is not more in circulation than the amount initially deposited.  I have a sense that this is economically meaningful.

Maybe I am wrong about all of this: If I am wrong in my conclusion, I welcome comments as to why and why it matters (don’t say “inflation”: you have a right to your property; you have no right to the value of your property).  Also, I welcome comments about what might be done about it – while respecting free markets, private contracts, the NAP, and private property.