I published two papers on SSRN based on my independent investigations into what I call "sources and sinks" of money.
Sources and Sinks of M1 Money in a Four Sector Model of the U.S. Financial System:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2257270
Financial Instrument Generation in the U.S. Financial System:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2458563
Every economic unit in the national economy can be classified using four sectors shown below:
Fed | Banks | ---> Generators of Money
Gov | Other | ---> Users of Money
In this model Gov means the Treasury branch of the federal government. Fed means the central bank also known at the monetary authority. State and local governments and all other non-bank units go into the Other sector.
Define M1 money supply as transaction accounts TA plus currency in circulation CC:
$ M1 = TA + CC$
When a bank makes a loan to Other, or when a bank buys financial securities (bills, notes, bonds) that were issued by Other or Gov, then this increases the M1 money supply as net new transaction accounts and increases Bank Credit in aggregate bank assets:
${\Delta}TA = {\Delta}BC$
Transaction accounts TA are bank liabilities. Banks develop Other Liabilities L* to keep reserve payments flowing in the interbank payment system even as the bank sector expands its balance sheet on both asset and liability side. The source of the Other Liabilities L* is the net reduction of TA:
$-{\Delta}TA = {\Delta}L*$
The delta notation means the net change in levels on the balance sheet of the aggregate bank sector over the accounting period used to keep the financial statistics.
A simplified model for the Bank sector balance sheet:
$ RB + BC = TA + L* + EQ $
When the economy expanded prior to the financial crisis of 2007 the pool of reserve balances RB, provided by the Fed to the Bank sector, did not grow in proportion to the huge rise in Bank Credit BC, so the ratio RB/BC became progressively smaller and smaller. Economist Hyman Minsky explains this in his book Stabilizing an Unstable Economy: the bank sector can economize on reserve balances RB by rolling over and expanding Other Liabilities L* and issuing sufficient equity claims EQ.
The bank sector creates the transaction accounts TA that convert to Other Liabilities L* and equity EQ. The Fed (central bank) must provide enough reserves to help the banks keep payments flowing, without being forced to sell some assets to Other sector, in order to hit their monetary policy goal of say 2% inflation. When money and credit markets are efficient and expanding credit Fed does not have to supply much reserve balances RB because banks try not to hold these non-performing assets. During the global financial crisis the Fed was forced to inject excess reserves and net transaction accounts into the Bank sector via Large Scale Asset Purchases (LSAP) because credit and money markets were frozen with distrust and this deprived the Bank sector of the ability to rollover and expand the sum of TA + L* + EQ necessary to hold the sum of RB + BC on the asset side of the balance sheet(s).