No, technically speaking they are not creating money.
On their balance sheet they are taking deposits and loaning a portion of it out while still offering demand deposits. As long as this isn't hidden from their depositors (and it isn't, read your contract with your bank) then there's no fraud and certainly no creation of money. But because these are demand deposits and because banks are FDIC insured and because they have a lender of last resort people don't read and understand their contracts with their banks and they don't know that their demand deposit is levered up to who knows how much so they ignorantly act in the market place as if there is more money when in fact all there is is loans being reloaned that are being reloaned that are being reloaned ect..
That's not true entirely. Let's say all I own is $5,000.- in cash. That cash is on the asset side of my personal balance sheet. On my liabilities side there would be either debt, or in my case net worth of $5,000. But what is this cash worth? In whose balance sheet's liabilities side is it listed? It is a liability of the central bank and it is backed by the central banks assets which includes gold, foreign currency, loans to commercial banks, claims against governments, etc. Let's say my $5,000 is all the currency in circulation, so the central banks asset side is worth $5,000.
Now I'm going to a bank and deposit that cash in a bank account. What has happened to my personal balance sheet? It has not changed in size. I still have a net worth of $5000, but my asset category has changed from "cash" to "deposits at commercial banks".
At the same time the banks liabilities side is increased by $5,000. It obviously has to find a way to balance it's books and the way the bank does that is by loaning out a certain percentage, say 90%, and either keep the rest as cash. I'd like to stress out here, that the banking sector would give itself a reserve requirement, even if they were not forced by law to do that. The reason for this is because the bank knows that a certain ratio of the deposits is cached on a regular basis and the bank doesn't want to risk a bankrun.
Now their asset side consists of $4,500 in loans to the new customer "A" and $500 of cash. Note in our example the bank loaned out the physical excess cash and didn't, as usual nowadays, create a new digital account, but we will soon see why that doesn't change much. "A" needed the loan to invest in a new machine. So machine manufacturer B is now in posession of the $4,500 and goes on to deposit this money to our commercial bank, thus expanding its balance sheet further by $4,500 of cash respectively deposits.
As we already know this process can go on and on until the commercial bank has all the initial $5,000 of cash reserves and $45,000 of loans on its asset side and deposits worth $50,000 on the liabilities side
without any form of central bank intervention at all.
This is obviously extremely simplified. Here, the only form of bank reserves is the cash held physically at the bank. As we have seen the bank can make the maximum amount of loans by keeping the reserves as low in comparison with it's loans as possible. In reality reserves consist of cash as well as deposits at the Federal Reserve System. These are also traded in the interbanking market on an overnight-basis at a rate called the Federal funds rate (some banks have excess reserves and others a shortage at the end of a day, depending on how good business was, so they trade those reserves).
However, at this point commercial banks cannot increase the money supply further. In theory they will also lend out as many loans as the reserve requirement allows them. And since the bank reserves consist of cash and deposits at the central bank and the only institution that is able to create those is the central bank, it ultimately controls the money supply (at least in "normal times"). If it wants to increase the money supply, it loans out additional money to commercial banks in so called "open market operations" (the fed funds rate used to follow the interest rates of these loans very closely). Those loans with a one week maturity, secured by government bonds or other assets, are credited to the banks' deposit accounts at the Fed, serving as newly created bank reserves, that can in turn be used to create a multiple of its value in loans/deposits for non-banking institutions (companies, governments, individuals).
