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I've been studying money creation recently and have come across some contradictory statements and different types of theories that I'd like to clear up.

  1. The classical theory of money creation which is the Fractional Reserve Model taught in textbooks whereby a bank gets a certain amount of deposits from the public, for example 100 billion, and has a reserve ratio of 10% would keep 10 billion in reserves and the rest 90 billion of deposits will get loaned out which would then end up in another bank which would then keep 9 Billion and lend out 81 billion and so on and on... until we end up with 100 bil / 0.1 = 1 trillion, where 900 billion new money was added to the money supply.

  2. However, according to different sources, including banks themselves, banks do not need or even touch your deposits when making out loans. In the case of not touching your loans are they trying to say that when a bank has 100 billion in deposits, this would be left untouched and be considered the reserves and since their reserve ratio is 10% they could in essence give up to 900 billion worth of loans. So on their accounting books it would look like 100 billion of deposits are reserves(this was the actual money that the public deposited in the bank) and 900 billion of deposits are loans (that is they created this credit on the basis that they have a 100 billion of reserves). And then you have some people like Werner who take this a step further and say that the banks aren't even limited by Reserve Requirements and can give as much loans as they want. So called "Thin Air" money with no limitations.

  3. Finally, everywhere I search up it is said that credit cards are not considered part of the money supply and thus when new credit(loan) is given this wouldn't be considered as money creation in the money supply. But how does that work? In both the previously discussed scenarios the giving out of loans is what contributes to the increase in money supply(money creation) so why are credit cards any different when they too are loans? Wouldn't credit card top ups just be considered part of the 90 billion in loans in Scenario 1 and part of the 900 billion in loans in Scenario 2

If someone could explain with an example with numbers of how money ACTUALLY gets created in our modern economies. I'd highly appreciate it. Thanks

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First, it is important to note that not all countries in the world have exactly the same monetary system. I will focus predominantly on how things work in US and EU. Other places might have some special nuances that are not covered here. Also already there are some differences between EU and US that I will try to highlight. In addition, I will focus on your point about constraints on money creation rather than going to every gritty-nitty detail.

In a current modern monetary system money can be created by either central bank or private banks. I think it is best to start with central bank because it is much more simpler. Afterwards I will build upon that with more complex system that operates in private banking.

Central bank money

Money that central bank creates are generally known as high-powered money or monetary base. This includes central bank reserves and money in circulation. Important note here is that while ECB (EU) can both create notes and reserves, Fed technically can only create reserves and notes are printed by Treasury (bureau of engraving and printing) but this is primarily done to satisfy orders from Fed (example here) and Fed member banks so de facto the money in circulation also depend on what Fed influences the amount of notes.

The money printing itself is the simplest way how new money can be introduced. Treasury (to fulfill orders from Fed) or in EU ECB simply turns out the money printer and prints notes, or they contract some mints to mint notes.

Second way how they can create more money is via issuing reserves. This is either done to purchase assets (e.g. government or sometimes even private bonds) or to lend it to private banks. This is probably the only time when you can really say that money is actually being completely created out of nothing without any restrictions (private banks cannot do that as explained below as they are constrained by central bank monetary policy and banking regulation).

Numerically this works as follows. If CB wants purchase some asset such as government treasury costing \$1000 they simply enter that \$1000 into their accounting ledger as a reserve. Next they deposit (electronically) \$1000 onto sellers account in exchange for the government treasury thus creating extra deposit. This extra deposit becomes new money.

If private banks borrow reserves from central bank pretty much the same thing occurs. Central bank creates \$1000 reserves on its ledger and then lends it to private bank.

Money Created by Private Banking Sector

Here I do thinking it is better to start with little history window. You are correct that the 'fractional reserve model' (properly known as multiplier model) does not describe current modern banking system. However, it provided good enough approximation till about 2009, at least when it comes to supply side as central banks would also indirectly affect money demand through interest rate.

At that time private banks faced biding reserve constraints, as you can see from this graph provided by Fed up until 2008 there were virtually no excess reserves meaning banks were effectively limited in how much loans they give in terms of reserves, and you could describe supply side of the system with that multiplier model. In such system there was clearly a constraint on money creation. I will skip quantitative example for this case as its not very interesting.

Post 2009 we moved to a new system when central banks expanded amount of reserves and in 2013 even started paying banks to keep reserves (see Federal Bank of San Francisco explainer). In this environment mechanism changed. While there was still de jure constraint in form of reserve requirement, since reserves were abundant they did not pose de facto constraint on bank lending at that time. This system is quite well described by (McLeay et al, 2014) paper that was already mentioned in other answers as well.

Quantitatively, following McLeay et al, an example of how money was created would be as follows. A customers comes to a bank asks for \$1000 loan. Bank would record \$1000 loan and \$1000 deposit. They would still need to comply with reserve requirement but since there were excess reserves a bank could always get more as they lent. So reserve requirement at that point was not effective constraint in terms of reserves.

This lead to some people inaccurately calming that private banks are creating money out of nothing. However, that was always a misconception. As mentioned in McLeay et al, banks were restricted by monetary policy, number of loans they can effectively give out depends on interest rates etc. However, even more importantly as pointed out by Rendahl & Freund (2019) (these authors also debunk the Weiner claims) bank lending is constrained since they create private money by liquidity transformation. That is by transforming an illiquid future ability to repay of borrower into a liquid bank deposits, and failure to do so would result in bank bankruptcy. A CB does not face such limitations, hence why I said in previous section that is the only case where you can talk about money being created literally without constraint.

However, the above is not how banking system operates today. In early 2020s reserve requirements were abolished, so private banks did not faced even the de jure constraint anymore. Nonetheless, they were now constrained by new liquidity and capital buffers (see Åberg et al 2021). For example, the liquidity coverage requirements require that bank has certain level of liquid assets for given amount loans that they make usually also weighted by riskiness. These liquid assets could be still excess reserves, but many banks also hold short term government bonds (as they are typically given zero risk weight and might be more interesting for banks to hold than reserves).

Using quantitative example, now banks can just issue loan where they just create matching deposit account to loan without worrying about reserves per se. So for example, now if someone requests \$1000 they will create \$1000 deposit, but then in turn they are required to get some liquid assets to satisfy the liquidity coverage ratio. The exact amount depends on liquidity inflows and outflows of the bank as well as on riskiness of loans and so on. So bank will have to set up some \$x aside in liquid assets (reserves, gov bonds etc), and this constrains bank lending.

In addition, the Rendahl & Freund (2019) explanation still applies. In fact, the recent SVB failure is good example of banks failing at the liquidity transformation. You can have a look at this excellent video-explainer by professor Boyle. In essence, the reason why this bank failed was precisely when they were setting aside liquid assets (primarily government bonds and very little to no reserves) they unwittingly exposed themselves to interest rate risk. This is because price of bonds depends inversely on interest rate. When the bonds fallen in value they simply didn't had enough liquidity their liquidity outflows. This illustrates both the constraint created by liquidity transformation (although this bank failed at it and thus got eliminated), but it also shows that banks really at least some cash deposits to operate and can't just create money willy-nilly.

PS: Regarding the credit card question, I think Fed explains it quite well in this explainer. M2 is defined in a such a way that we do not include loans only assets, so also in the examples above money would be crated when deposit is created loan is just a counterbalance to that deposit. I recommend reading that explainer for more details.

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@Mick probably offered the best answer by linking the BOE paper. I'll try to address your questions more directly.

Point 1) It is an outdated and simplistic model. It assumes loans, which are typically long-term and illiquid, are financed via deposits that are short-term and liquid. Even if all banking would work like that, you would not get the maximum amount you compute unless everyone involved (the person who receives the money form the loan, the next bank, the next person who gets the loan and so forth) were to always only keep the minimum needed and deposit every proceeds.

Point 2) Many central banks, including the FED eliminated reserve requirements (or never had any in the first place) for all depository institutions.

Point 3) you are mixing up money with credit. Money is an asset for whoever holds it. Credit on the other hand is a liability and never money. Just like loans are not money but liabilities.

So what happens really? Money in its pure form comes from a high powered institution (The U.S. Department of the Treasury prints money and mints coins, the FED creates money by buying bonds from banks and transferring money to an account at the bank).

Commercial banks increase this monetary base with loans etc. Among other things, commercial bank must satisfy liquidity ratios (LCR, NSFR, certain interest rate risk limits etc). Within this framework, as long as there are enough liquid asset, the bank can provide loans. And other services. As assets, it can use central bank money (obtained via all sorts of channels), issue it's own bonds (nowadays mainly covered bonds that are secured with assets), hold government bonds and other liquid assets etc.

For short, there is no simple formula that would show you how much money will be created in the banking system.

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  • $\begingroup$ Your Point 3 is confusing me because it is said everywhere that it is precisely this loaning out of money that contributes to an increase in Money Supply(which is a different way of saying Money Creation). So I can't seem to understand why Credit Cards(which are also a type of loan) aren't considered to expand money supply. $\endgroup$
    – ayazasker
    Mar 14, 2023 at 18:26
  • $\begingroup$ A loan is a liability like credit card debt but it simultaneously creates a matching deposit in the borrower's bank account. That is the money. The loan itself is not. $\endgroup$
    – AKdemy
    Mar 14, 2023 at 19:00
  • $\begingroup$ If you have a loan you should see the loan separately in your app and usually the deposit is long gone (you paid for something). It ended up being a deposit somewhere else and that's the idea of money creation according to point 1, because that deposit can be lent out again. $\endgroup$
    – AKdemy
    Mar 14, 2023 at 19:10
  • $\begingroup$ When I pay for something with a credit card does it not end up being a deposit somewhere else though? Say I bought a 1000 dollar phone through my credit card. That 1000 ended up as a deposit in the phone shop owners account did it not? $\endgroup$
    – ayazasker
    Mar 14, 2023 at 19:14
  • $\begingroup$ I recommend you read the BOE article. It discusses credit card transactions too. Ultimately, your credit card debt is very short term and destroyed as soon as you pay back each month. Bottom line though is that credit cards (as well as loans) are not money itself. Especially if you top up your credit card (which means you prepaid it). $\endgroup$
    – AKdemy
    Mar 14, 2023 at 19:25
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There are a wide variety of things you can read that purport to explain our monetary system. It has been a controversial area. May I suggest you read the paper "Money Creation in the Modern Economy". It was published by the Bank of England in 2014 and has over 1600 citations according to Google Scholar. I think this is the closest you will get to a definitive explanation.

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  • $\begingroup$ that paper does not really describe current post-fractional system it only applies to the system that existed between 2009-2020 $\endgroup$
    – 1muflon1
    Mar 14, 2023 at 19:23
  • $\begingroup$ There are indeed continuous modifications made by regulators but I would suspect that 99% of the words in the BoE paper are true to this day. Feel free to suggest a better document if you think it exists. $\endgroup$
    – Mick
    Mar 14, 2023 at 20:18
  • $\begingroup$ we are not talking about continuous modification, the 2020 rework of financial system was quite fundamental, it is definitely not 99% accurate given that the paper goes into details that changed fundamentally, some broad conclusions can still hold but the details and diagram in that paper are no longer accurate at all $\endgroup$
    – 1muflon1
    Mar 14, 2023 at 20:23
  • $\begingroup$ As I said, "Feel free to suggest a better document if you think it exists." $\endgroup$
    – Mick
    Mar 14, 2023 at 20:31
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    $\begingroup$ @Mick You can add links to your comments by writing [ text to display ] ( URL ) without the spaces. E.g.; link to the new question. $\endgroup$
    – Giskard
    Mar 14, 2023 at 20:51

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