|George Bailey (James Stewart), Mary Bailey (Donna Reed)|
and their youngest daughter Zuzu (Karolyn Grimes). [A]
It's 10:05 am and you, as owner/manager of Bailey Building and Loan Association, are sitting at your desk.
You are happy and relaxed: life's wonderful, just hunky dory. As a conscientious banker, you make sure Bailey B&LA complies with all legal requirements and standard accounting practices.
Suddenly, young Bo Anderson comes along, sweating and slightly short of breath. Without knocking at the door or even greeting, Anderson says:
"Mr. Bailey, sir, I need ya help. I wanta buy Old Sven's house and I need $900. I'm gunna get married to Mary Ellen Walton and we need a house".After Anderson explained himself, you, as Bailey's main and only credit analyst, give Anderson the loan.
Anderson, more relaxed now, manages to smile and, before leaving, turns and says with manifest gratitude:
"Ma was right. She always tells me to go talk to George Bailey, that he's a good man".After Anderson leaves, as Bailey's CFO, head accountant and only bookkeeper, you open the books and write down the transaction:
Assets | Liabilities | Net equity
+$900 | +$900 |
With this transaction, Bailey's assets (the Anderson loan, represented, say, by a mortgage) increased by $900. You opened an account at Bo's name, with $900 (the money he'll use to buy the house). That's a liability for Bailey's. As both assets and liabilities increased by the same amount, Bailey's net equity did not change.
What about Bo Anderson? For him Bailey's asset is a liability; and Bailey's liability is an asset. Bo's net equity hasn't changed, either.
Similar scenes are happening all across the State of New York, or even the US.
All the B&LAs giving loans to buy houses, and all the Bos, Joes and Jacks buying them with the money thus raised, saw their assets and liabilities go up. That's true.
But their net equity? It didn't change: not one B&LA saw their net equity increase, just like Bailey's net equity did not increase. And exactly the same happened to all the Bos, Joes and Jacks.
Before proceeding, notice what happened here exactly: a loan was given, a double-entry transaction was inscribed in a book. Nothing else. In particular, the loan was given, but no previous depositor was mentioned.
Now, let's consider two separate issues: (1) Bailey's need to comply with fractional reserve legal requirements and (2) Bo's use of the money he's just gotten.
George Bailey and Fractional Reserve
After writing down the transaction above, George Bailey (you) finds that both Bailey's loans (assets) and deposits (liabilities) went up by +$900.
If depositors never withdrew money from their accounts and banks didn't exist to make profits, that would likely be the end of the story: Bailey's did create deposits "out of thin air", by a simple double-entry bookkeeping operation.
Alas, people don't keep money in a bank's account without a purpose: sooner or later, they'll want their money back. And banks lend money for a profit.
Over banking history, this has caused some difficulty: if a bank's depositors came all together to withdraw their money, the banker wouldn't be able to return it to them. To avoid it, and following the law, George Bailey need's a reserve in liquid assets (let's say, cash).
Strictly speaking, no bank (or B&LA) can ever reduce this risk to zero. To achieve this they could not lend anything: their deposits would need to be sitting there idly by. But, if they couldn't lend any money, how would banks make any profits?
As a rule of thumb and compromise, the amount loaned by a bank must be a fraction of the deposits it keeps. Let's say, 90%. 10%, therefore, needs to be kept as a reserve. Incidentally, notice that all these considerations are not originated in double-entry bookkeeping: it's a legal imposition.
So, if at a given moment your deposits add up to $10,000, then you can have at most $9,000 in loans. The remaining $1,000 deposited are kept as reserve. And this is all the law requires of a banker. In principle, how you achieve that is up to you (but central banks will give you a little hand, as we'll see soon).
Bailey's has a new deposit ($900) and a new loan ($900), but no additional reserves: Bailey's reserves and deposits might be $100 short. But there's no need to panic, yet. George Bailey needs to check the books.
Maybe he finds he's already got the $100: perhaps yesterday, just before locking the door for the day, Giuseppe Martini (George's good friend), came in and deposited $100. In that case, the money was just there waiting to be used as reserve (not waiting to be loaned!) and George can recline his chair, light up a Camel, cross his hands over his belly, put both feet on the desk, and say: "It's a wonderful life".
Before moving on, let's recap: the Anderson deposit was still created "out of thin air", this did not change. It was this eventual previous deposit (Martini's) that was actually backed up by some form of cash. The whole deposit was used as reserve.
What if Martini (or another customer) did not deposit any money previously? No biggie. Henry F. Potter (Bedford Falls' wealthy slumlord and general purpose nasty guy) or another customer could still come by and deposit the amount required.
For that matter, perhaps George, himself, could deposit some money in his own account. Or he could call another B&LA or bank and ask for a loan.
Ultimately, all else failing, he can ask for a Fed loan. That's one of the things a lender of last recourse does.
Whatever happens, this is what the book shows at the end of the day:
Assets | Liabilities | Net equity
+$900 | +$900 |
+$100 | +$100 |
The $100 under assets is the addition to reserves, the $100 under liabilities is the new deposit, regardless of its origins (other depositors, other banks, George's own pocket, the Fed). Considering all the day's transactions, we have $900 in new loans and $100 in reserves (totaling new assets for $1,000), and $1,000 in deposits (i.e. liabilities): Bailey's complies with the law.
Bailey's did not need to have the deposits before making loans. It could have happened, but it wasn't necessary. 
More generally: not every single deposit needs to keep the 90%:10% ratio prescribed by fractional banking. Because of this, Bailey's created money "out of thin air" even in the presence of fractional reserve banking.
And this is a general principle: not a single bank needs to wait until they have a deposit to lend 90% of it. That's not what fractional reserve banking forces banks to do. So, no money multiplier, thank you very much.
When Old Sven deposits in his own account the $900 Bo paid him, neither Bailey's nor any other bank needs to put $90 in the freezer, leaving $810 for future loans. They can just lend the entire $900 or more, if they can, in the reasonable expectation that they could get the reserves required. 
But there's something more: aggregate assets and liabilities increase equally, alright. But we can't say that Anderson ultimately owes money to any individual. Because the $900 were created "out of thin air", out of the $900 Bo got, not a cent can be traced back to individuals. Bo owes money to Bailey's.
More generally, it's not true that a household's liability means another household's asset. If a macroeconomic model (whether one calls it NK, NC, KKK or KGB) is based on this assumption, then one can say "Houston, we've gotta problem".
Now, we leave good old George Bailey and drop by Bo Anderson's newly-bought house.
As we've just heard, Bo paid Old Sven for his house. His equity did not change by doing that: he still owes Bailey's $900 (that is a liability for Bo) and has an asset (the house) with a market value of $900. Net equity: $0.
But, let's remember that many Bos, Joes, and Jacks, all over the place, are buying houses. Perhaps housing prices start to go up! If that's the case, Bo could soon be getting capital gains. Bo's net equity could be increasing.
This is not a direct consequence of double-entry bookkeeping, and sometimes, rightly or wrongly, this is the impression one gets when this phenomenon is explained by Prof. Keen's followers.
It's just that the liability Bo acquired is used to finance the acquisition of a physical asset. In other words, in the case of housing, debt is used to fuel demand in the so-called "real" economy. If the supply is less than the demand, prices could go up.
The other side of the coin is that house prices (against what many Aussies believe) sometimes go down: in that case, Bo could end up underwater. D'oh!
This is my account of what Steve Keen has been trying to explain in his recent debate with Paul Krugman.
I cannot guarantee the account is 100% faithful to Prof. Keen's teachings, as I've followed him only irregularly, but it's my honest understanding of what he says.
And, at least to me, it doesn't sound nonsensical or "mystical", which is an adjective Prof. Krugman used to describe Prof. Keen.
But it is a simplification, as footnote 2 makes clear.
I also deliberately chose "George Bailey", an extremely likeable fictional banker, who follows the rules to the letter and is not desperate to make a quick buck.
And if even George Bailey can and would lend "out of thin air", it seems utterly naïve to assume real bankers can't.
Those are my two cents, anyway.
[A] George Bailey (James Stewart), Mary Bailey (Donna Reed) and their youngest daughter Zuzu (Karolyn Grimes), from the motion picture "It's a wonderful life". Wikipedia.
 In fact, George would be negligent and Bailey's could go broke if that was the usual situation: Bailey's can't afford having too many unproductive interest-earning deposits.
 Strictly speaking, this is only true if there were no other constraints. But there are: often banks face constraints relating loans to capital, for instance. Or related to obtaining financing from other banks or large institutional investors. One such constraint could force a bank to deny or postpone loans. And, even though this needs to be taken into account, these additional constraints generally only qualify the general principle: banks can lend as much as they want.