Money matrix

Whether the money is physical or digital; whether centrally issued by fiat, or mined by the market in a decentralized manner, this table specifically refers to the post-Bretton woods, floating fiat currency system, as there is no further ‘redeemability’ for basic money at banks and central banks.
Here we see that ‘Inside money’ and ‘Claims’ are tightly related. Some notes on this. First, the entire categorization of ‘Inside money’ is named as such because it comprises monetary ‘Claims’ that are issued ‘Inside’ the banking system. A simple example is checkable deposits, or demand deposits, issued by banks. Those claims are redeemable back into ‘Outside money,’ which is ‘Outside’ the financial system. Historically, such ‘Outside money’ was gold and silver. Today, ‘Outside money’ also includes the fiat Monetary base (and is also analogous to bitcoins). This ‘Outside money’ today is indeed not a claim. Notice, however, in the Monetary base column, in the context of fiat money, we see that fiat is comprised of all physical ‘Notes and coins,’ as well as the digital ‘Commercial bank reserves,’ both of which today are solely issued by the central bank. In the financial system that existed pre-1933 (domestically, in the United States), and pre-1971 (internationally, across central banks), this fiat monetary media itself could actually be redeemed for gold and silver! Thus, in earlier days, that monetary media was a claim. However, after a permanent ‘suspension of specie’ (first in 1933 for Americans and then finally in 1971 for the entire globe), no bank or central bank would ‘redeem’ this fiat monetary media for anything at all. Therefore (and as stated, the above table is referencing the current financial system), economists and central banks now refer to this fiat monetary media as ‘Basic money’ or the ‘Monetary base.’ It is the end of the line in the banking system, as no further claims can be made against them, and they can’t be redeemed for anything else. Thus, we refer to all of this ‘basic,’ monetary media (gold and silver historically, government fiat today, and potentially bitcoins, in the future) as Outside money—originating ‘Outside’ the banking system. Now, one final note back on ‘Inside money.’ In economic lexicon, we see that it is comprised of the various ‘Ms’—M1, M2, and M3. All of this monetary media are claims and indeed ‘Inside’ the banking system. However, notice that ‘M0’ (physically currency that is outside bank vaults and the central bank) is also a part of M1 (and thus M2, and M3)! Even with all of our categorizations today that economists make, there isn’t always a clean break between what is ‘Outside the banking system,’ and what is ‘Inside the banking system.’
In any banking or financial system, past or present, the Monetary base is the ‘end of the line.’ It is the monetary asset of ultimate settlement, and it cannot be ‘redeemed’ for anything else. Note this does not mean it can’t be pledged as collateral for lending and borrowing; rather, it simply means it is the irredeemable and ultimate asset of settlement of any banking system.
Since 2017, Bitcoin has enabled ‘locking’ UTXOs from the main chain to balances on the Lightning Network, balances which in turn can trade much faster on said network than on the main chain. No single entity is in charge of nor issues these balances; it is entirely decentralized. This is, indeed, a unique stock of money in the history of economics, offering less assurances than on-chain bitcoin UTXOs (basic money), yet more assurances than any ‘claim money’ or ‘deposit money’ (M1 and above). Therefore, one can think of bitcoin balances on the Lightning Network as bitcoins with ‘slightly less assurance’ than basic money, on-chain bitcoins, yet basic money nonetheless.
This money supply is unfortunately not typically delineated; however, it is extremely important. This money supply in total comprises what is known as ‘reserves’ in the numerator of the ‘reserve ratio.’ The Reserve ratio is defined as these reserves divided by the total outstanding amount of bank demand deposits at any given time in the banking system. Central banks across the world have many different reserve ratios mandated for their member banks, and sometimes none at all.
Another way to define M0 is ‘Currency in circulation.’ If you added M0 to Basic money inside banks, you would arrive at the Monetary base. These money supplies are all inter-related, and they are all different supplies of basic money. Typically, when we speak of M0, we are speaking of physical currency that resides outside banks; however, it is presumed that with the emergence of both bitcoins and CBDCs, the majority of these digital monetary instruments will be classified into M0 as well (more below).
CBDCs are in their infancy; and as they take their cues from Bitcoin, they are obviously younger than Bitcoin itself. If ‘Digital wallets’ continue to emerge as a regulated monetary media in the financial system, then both CBDCs (by fiat) and bitcoins (naturally) will be included in this M0 money supply. However, the question will arise as to which portion of this basic money will be ‘inside banks,’ and which portion will be ‘outside banks.’ With bitcoin UTXOs, it is perennially obvious—the UTXOs are either controlled by entities inside the financial system (such as cryptocurrency exchanges, analogous to ‘Basic money inside banks’), or outside the financial system (privately holding one’s keys, analogous to ‘M0 money’). A reminder, after adding those two money supplies together you will always arrive back at the Monetary base. Yet with CBDCs, though an individual may be allowed to hold CBDCs in their own digital wallet, that very wallet will clearly be controlled by banks in the system (if not the central bank itself). Note we are not trying to arrive at what portion of the money is ‘censorable’ (it is 100% censorable, in the case of CBDCs); rather, we are trying to arrive at which portion of the money is available to sit as ‘reserve’ for financialization and lending. Time will tell what regulations guide certain CBDCs in digital wallets to sit as ‘reserve’ versus being ‘M0 money.’
The supply ‘Demand deposits’ generally refers to checking accounts held at commercial banks. Typically this will also include other ‘checkable deposits’ with similar characteristics held at credit unions and other financial institutions. Note that this money supply is the denominator in the ‘Reserve ratio’ described above.
Since 2015, Tether Holdings Limited (and subsequently many other companies) have launched ‘stablecoin’ protocols on various blockchain networks. These coin balances have proven resilient and trade like bitcoin UTXOs; however, these units have the distinct economic difference of being issued by centralized entities, and ‘backed’ by investments (fiat cash, bonds, etc.). Yet these units are also more democratic than other forms of traditional money stocks (as retail and institutional buyers alike can easily hold them), so they could be categorized as anything from retail deposits to institutional money market funds. However, stablecoins also have the additional, distinct difference of being issued outside of the (typically US) banking regulatory framework, so in that sense they are similar to eurodollars (foreign-based US dollar accounts). For each and all of these reasons, stablecoins could be classified under a variety of money supplies, from ‘on demand’ claims (M1 money), to less liquid, retail or institutional ‘at interest’ or ‘staked’ money (M2 / M3 money), yet specifically outside the purview of the banking system (eurodollars / M3 money).
If we look at the history of the term ‘eurodollars,’ it developed with the emergence of a large presence of US dollar-denominated bank deposit balances demanded after World War II, primarily held in European banks. These banks honor claims in dollars, yet are outside the jurisdiction of the Federal Reserve. For these reasons, eurodollars were classified into M3. Note that the term has nothing to do with the ‘euro’ currency itself. Other central banks (though not all) compile estimates of their respective ‘eurodollars’ (meaning ‘eurosterling’ or ‘euroruble’) in their broader money supplies, typically above M3. Again, though the term ‘eurodollars’ specifically applies to foreign-held US dollar claims, the general idea is that it reflects a local central bank’s broader money supply (any currency) that is located in foreign jurisdictions (again, claims only).

As can be seen above, a consistent and strict accounting of various monetary base and bankers’ claims supplies of money can get really complicated, really quickly. It’s important to be rigorous. It’s also important to remember that all of the information above explains the various money supplies in a globalized manner. These are generalities, and they are not rooted in the definitions of any particular country.