fractional-reserves = 'demand-side' stimulus?

[Widdekind]

"toy model" of fractional-reserve banking

S = "Savings" rate (into banks)
S* = (1-S) = "not Saved" rate

F = "Fractional-reserve" requirement (used by banks)
F* = (1-F) = "not reserved" rate​

"inside" -- how much money remains "reserved" in banks ?

S* not saved, S saved...
of S, SF* not reserved (loaned back out), SF reserved

of SF*, SF*S* not saved, SF*S saved...
of SF*S, SF*SF* not reserved (loaned back out), SF*SF reserved

of SF*SF*, SF*SF*S* not saved, SF*SF*S saved...
of SF*SF*S, SF*SF*SF* not reserved (loaned back out), SF*SF*SF reserved​

by extrapolation, after an infinite sequence, of "savings; re-lendings & re-savings", the final fraction remaining reserved, in banks, becomes

= SF + SF(SF*) + SF(SF*)^2 + ...

= SF [ 1 + (SF*) + (SF*)^2 + ... ]

= SF / [1 - (SF*)]​

"outside" -- how much money remains "un-saved" in circulation ?

S* not saved, S saved...

of S, SF* not reserved (loaned back out), SF reserved
of SF*, SF*S* not saved, SF*S saved...

of SF*S, SF*SF* not reserved (loaned back out), SF*SF reserved
of SF*SF*, SF*SF*S* not saved, SF*SF*S saved...​

by extrapolation, after an infinite sequence, of "savings; re-lendings & re-savings", the final fraction remaining un-saved, in circulation, becomes

= S* + S*(SF*) + S*(SF*)^2 + ...

= S* [ 1 + (SF*) + (SF*)^2 + ... ]

= S* / [1 - (SF*)]​

"reality check"
Fractional-reserve banking "fabricates" no new money; the total fractional amount remaining, both in circulation, and reserved in banks, becomes:

= SF / (1 - SF*) + S* / (1 - SF*)

= (SF + S*) / (1 - SF*)

= (SF + [1-S]) / (1 - S[1-F])

= (1-S+SF) / (1-S+SF)

= 1​

Fractional-reserve banking reduces "hoarding"
without banks, the ratio, of money still in circulation, to money reserved in banks, would be

S* : S​

with banks, using Fractional-reserves, the ratio increases, to:

S* : SF​

for example, if S = F = 0.1, then Fractional-reserves reduces "hoarding", from ~10%, to ~1%. Ipso facto, Fractional-reserve banking:

• does not "fabricate" Money
• does reduce "hoarding", i.e. "accelerates" otherwise-zero-velocity Money ("that's how bankers make their Money")

De facto, Fractional-reserve banking "taps hoards", "accelerating" the maximum amount of otherwise-zero-velocity Money ("bankers know best"), effecting ideal "demand-side" stimulus; additional "demand-side" efforts are forecasted to fail ("bankers knew best").

 

[DSGE]

Not really in the spirit of what people are complaining about.

What you've done is looked at how much base money there is under fractional reserve. Some of it is held as reserves, some of it is held by the public. If we start of with a monetary base of 1, what you've done is show how it gets divided between reserves and currency held by the public. Obviously it has to sum to 1 since the monetary base is set by the central bank.

What people are interested in is not the monetary base, but broader measures of money. The base is currency + reserves. The "money supply" people care about is currency + deposits. The problem people have (though it's a ridiculous problem) is that they feel that deposits should equal reserves. That is, base money shouldn't "multiply" into several deposits.

 

[Widdekind]

base [money] is currency + reserves. The "money supply" people care about is currency + deposits... they feel that deposits should equal reserves [i.e] base money [reserves] shouldn't "multiply" into several deposits.

for centuries, bankers have re-circulated "savings", putting "idle" money into "motion", so "stimulating" their economies, with ideal "demand-side" policy; as long as all loans are good, at worst "savers" would "have to wait a-while" whilst their money is called back; their "farmed-out savings" better their economy ("for the greater good", "bankers only profit, b/c others profited")

"banking" on their experience, FRs plausibly "accelerate" the maximum amount of "stationary" money; additional "demand-side" efforts, by Government, implausibly improve upon bankers' "best efforts"; FRs seem similar to "time shares [on money]"

(In other threads, "Leftists" argue that wealthy people "have more money than they need", and so can afford high Taxes; FRs grant access to "other people's money", without taking the money away from them. How can the latter be worse, than the former ?)

 

[Widdekind]

"toy model" of fractional-reserve banking

S = "Savings" rate (into banks)
S* = (1-S) = "not Saved" rate

F = "Fractional-reserve" requirement (used by banks)
F* = (1-F) = "not reserved" rate​

"deposits" vs. "reserves"

S* not saved, S saved...

of S, SF* not reserved (loaned back out), SF reserved
of SF*, SF*S* not saved, SF*S saved...

of SF*S, SF*SF* not reserved (loaned back out), SF*SF reserved
of SF*SF*, SF*SF*S* not saved, SF*SF*S saved...​

by extrapolation, after an infinite sequence, of "savings; re-lendings & re-savings", the final fraction alleged as "deposits" becomes:

= S + S(SF*) + S(SF*)^2 + ...

= S [ 1 + (SF*) + (SF*)^2 + ... ]

= S / [1 - (SF*)]​

Fractional-reserves became

= SF / (1 - SF*)​

ratio of "deposits" to "reserves" becomes 1:F. For example, if S = 0.1, then D2R = 10:1 ("FR banking 'monkeys with money'").

Sum of "circulation" plus "reserves" equals 1; sum of "circulation" plus "deposits" becomes

= S* / (1 - SF*) + S / (1 - SF*)

= (S* + S) / (1 - SF*)

= 1 / (1 - SF*)

> 1​

e.g. if S = F = 0.1, then nominal fractional "money supply" is ~1.1 > 1. However, nominal "money supply" does not cause inflation, because only actual "money in circulation" affects Prices (MV = PQ); FRB does increase "money in circulation" (S* --> S* / (1 - SF*), e.g. 0.9 --> 0.99), but not as much as apparently perceived (--> 1/(1-SF*), e.g. --> 1.1).

 

[Ariux]

"toy model" of fractional-reserve banking

S = "Savings" rate (into banks)
S* = (1-S) = "not Saved" rate

F = "Fractional-reserve" requirement (used by banks)
F* = (1-F) = "not reserved" rate​

Are you autistic?

 

[Widdekind]

FRB systems "lose no money" ?
in an FRB system, every dollar brought into banks, as Savings (S), ultimately stays within the system ("as it should"), as Reserves (R = S); but, the banks "play hot-potato" with that dollar, "letting lots of people look at it", so that the nominal value of alleged Deposits (D) exceeds the value of actual Reserves (R << D), according to the FR requirement (R = fD, D = R/f). Again, as a system, FRB "loses no money", so that the dollars brought into banks as Savings (S) all become Reserves (R = S), for all the loaned Deposits (D >> R = S):

f = reserve fraction
f* = 1-f

1 dollar deposited
f = reserves, f* = re-loaned
of f*, ff* = reserved, f*f* = re-loaned
of f*f*, ff*f* = reserved, f*f*f* = re-loaned...

total reserves
R = f + ff* + f(f*)^2 + ....
= f ( 1 + f* + (f*)^2 + ...)
= f / (1 - f*)
= f / f
= 1​

thus, after an infinite sequence of "savings & re-lendings", every original dollar brought into the system, remains within the system, albeit "spread way around", as "pennies, nickels & dimes" of Reserves, for many dollars worth of nominal Deposits. In practice, money saved may not be repeatedly re-loaned-and-then-re-saved; if not, then the Reserves, remaining within the FRB system, may be allot less, than original Savings (fS < R < S).

assuming infinite re-lendings & re-savings, reported Reserves equals total original Savings depositings:

if so, then after c.2008, "everybody brought their money to banks, and left it there"



fraction of "Saved" USD has plummeted ?
if every dollar brought into the FRB system remains within said system, albeit "spread way around"; then the fraction of USD "saved" can be estimated:

s MB = R
s = R / MB​

so estimated, s has plummeted from over 35%, to under 5%

however, a decline in the frequency of "re-lending & re-saving" could also reduce that statistical ratio ("after the first guy saves, the next guy borrows, and walks away with the money")