Banking Example #8: Treasury Deficit Spending

This example illustrates what happens when the Treasury department deficit spends (this includes auctioning bonds and then spending the proceeds). The core of this process is illustrated on balance sheet sets 2, 3, and 4 (debt auction depicted on the transition from 2 to 3, and spending the proceeds on the transition from 3 to 4).

Setup: the Treasury Dept. (Tsy), the central bank (CB), a commercial bank (A), and two people, x (Peter), and y (Paul). There are no reserve or capital requirements, and all balance sheets start off clear except that person y owns a house*.

1. Initial balance sheets for all players:

Tsy, CB, A, x

Assets	Liabilities
$0	$0

Person y

Assets	Liabilities
$100k house	$0
Negative Equity	Equity
------------------	$100k

 2. Balance sheets after person x takes a loan from Bank A and buys person y's house with it (this step, with a bank deposit in the private sector's hand, can be considered the initial setup for the deficit spending process):

Tsy, CB

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$100k mortgage to x	$100k deposit for y

Person x

Assets	Liabilities
$100k house	$100k mortgage at A

Person y

Assets	Liabilities
$100k deposit at A	$0
Negative Equity	Equity
------------------	$100k

3. Now person y decides to use the proceeds from the house sale to invest in Treasury bonds (T-bonds) from Tsy (say through Treasury Direct):

Tsy

Assets	Liabilities
$100k CB deposit	$100k T-bonds

CB

Assets	Liabilities
$100k loan of reserves to A	$100k deposit for Tsy

Bank A

Assets	Liabilities
$100k mortgage to x	$100k reserve borrowing from CB (mortgage used for collateral)

Person x

Assets	Liabilities
$100k house	$100k mortgage at A

Person y

Assets	Liabilities
$100k T-bonds	$0
Negative Equity	Equity
------------------	$100k

4. Tsy spends all the proceeds from the bond sale on services provided by person x to the government. The resulting balance sheets are:

Tsy

Assets	Liabilities
$0	$100k T-bonds
Negative Equity	Equity
$100k	----------------

CB

Assets	Liabilities
$100k loan of reserves to A	$100k reserve deposit for A

Bank A

Assets	Liabilities
$100k mortgage to x	$100k reserve borrowing from CB (mortgage used for collateral)
$100k reserves	$100k deposit for x

Person x

Assets	Liabilities
$100k house	$100k mortgage at A
$100k deposit at A	----------------------
Negative Equity	Equity
--------------------	$100k

Person y

Assets	Liabilities
$100k T-bonds	$0
Negative Equity	Equity
------------------	$100k

5. Finally Bank A pays back its reserve borrowing from the CB. The resulting balance sheets are:

Tsy

Assets	Liabilities
$0	$100k T-bonds
Negative Equity	Equity
$100k	----------------

CB

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$100k mortgage for x	$100k deposit for x

Person x

Assets	Liabilities
$100k house	$100k mortgage at A
$100k deposit at A	----------------------
Negative Equity	Equity
--------------------	$100k

Person y

Assets	Liabilities
$100k T-bonds	$0
Negative Equity	Equity
------------------	$100k

One way to interpret what happened during this Tsy deficit spending sequence (covered by the balance sheets illustrated in steps 2 through 5) is that Tsy deficit spending resulted in person y's bank deposit being redistributed to person x, and in the process person y was issued a net financial asset (NFA) (in this case the T-bonds). This is the usual pattern for Tsy deficit spending when the Tsy spends all of its proceeds and it must fund its CB deposit prior to spending (as in the USA) and it must turn to the private sector for this funding (also the case in the USA). Keep in mind that the only players here that can and do have CB deposit accounts are the Tsy and Bank A. That is why Bank A (person y's bank) must facilitate the funding of Tsy even though person y purchased the T-bonds through the Treasury Direct program: behind the scenes, and invisible to person y, Bank A borrows reserves from the CB (using its assets, in this case x's mortgage, as collateral) and transfers this CB deposit (reserves) to Tsy. What's the upside for Bank A in doing this? It get's to erase y's deposit from the liabilities side of its balance sheet. Also note that Tsy can only spend from its CB deposit, and to do this it transfers its CB deposit to the payee's bank (Bank A in this case), and the bank in turn credits the payee's bank deposit (person x's deposit in this case). Note that CB deposits held at commercial banks are called "reserves" while those at Tsy are not.

6. Now we examine one additional step: person x repays his loan (this step is not part of the deficit spending process, but it's useful in clarifying how equity, in the form of NFAs, are moved from Tsy to the private sector):

Tsy

Assets	Liabilities
$0	$100k T-bonds
Negative Equity	Equity
$100k	----------------

CB & Bank A

Assets	Liabilities
$0	$0

Person x

Assets	Liabilities
$100k house	$0
Negative Equity	Equity
------------------	$100k

Person y

Assets	Liabilities
$100k T-bonds	$0
Negative Equity	Equity
------------------	$100k

Notice how the non-bank private sector (persons x & y aggregated together) have obtained an NFA (the $100k T-bonds) as a result of Tsy deficit spending and the Tsy now has negative equity in this same amount (the government's debt). The overall result is as if Tsy just "printed" the T-bonds and handed them to the non-bank private sector in exchange for services the private sector performs for it. Meanwhile, bank A's and the CB's balances sheets are unchanged from the initial step 1. Also note, that like in step 1, no bank deposits exist after this step (making it a little easier to compare with step 1.).

*Why have person y start off owning a house? No particular reason. I was going to have person y simply perform some service for person x (like I usually do) but thought I'd change it up a bit. Plus that gives the bank a nice "mortgage backed security" (i.e. the mortgage itself) as collateral for borrowing reserves from the CB... perhaps moving the needle an incremental bit towards a more realistic example. Ha!

The Three Places Reserves Can Go

This post is very similar to my previous list of ways in which reserves can leave the banking system, but here I'm not worrying about what's inside or outside the banking system, which greatly simplifies matters. Also keep in mind that the titles to both this post and the prior one are technically incorrect and misleading: by definition reserves are base money INSIDE the banking system, so they can't go anywhere outside of it. Basically there's only three places reserves (really the base money that makes up the reserves) can go (not making a distinction between required and excess reserves here):

1. To an entity with a Fed deposit account: Treasury, GSEs, banks (foreign and domestic), foreign central banks, IMF, etc. Note that private individuals and non-bank businesses and organizations don't have Fed deposit accounts, and thus reserves cannot go to them*. Also note that not all banks (for instance) have reserve accounts either.
2. Withdrawn from commercial bank customer deposits as paper bills or coins, in which case they cease to be reserves (vault cash). They return to vault cash reserve status once they're redeposited at a bank.
3. Back to the Fed (central bank), where they are annihilated**. This is because reserves are liabilities of the Fed***. Electronic reserves are literally annihilated. Paper bills and coins, of course, might not physically be "annihilated" but instead might be sold again (i.e. exchanged for electronic reserves) to another bank. Of course they might also be literally annihilated (i.e. taken out of circulation permanently due to wear and tear).

Please see my other post for more details and an explanation of terms used here!

*Reserves can be credited to the bank where a private individual or non-bank business or organization holds its account with the bank instructed to in turn credit the private non-bank entity's deposit. This happens, for instance, when the Treasury pays a non-bank individual or business for services to the government from its Treasury General Account (TGA) Fed deposit (Note that funds held in the TGA and other non-bank Fed deposits are not technically "reserves" unless they are transferred to banks). It also happens when banks pay for goods or services or when they pay salaries or dividends to private non-banks when the non-bank recipients of the funds hold their deposit accounts at other banks. Note that in both cases, however, Fed deposits don't disappear: they simply move from one Fed deposit to another. Also note that this doesn't mean that banks can "loan out reserves" to non-banks. That's not how commercial bank lending works. I suppose you could claim that reserves could be loaned out indirectly in this manner, but that's always the case, even when there are no excess reserves in the system: when there are no excess reserves in the banking system, commercial banks will simply borrow the needed reserves from the Fed... and the bulk of this borrowing is on a very temporary basis (the exception being required reserves needed, by regulation, to support expanding commercial bank demand deposits). This is because the Fed (central bank) ALWAYS provides the reserves (if needed) to transfer deposits, clear payments, or expand the deposit base. That's one of the main things it's chartered to do! Also, if it didn't, it couldn't control the overnight rate (one of the other main things it does). Thus having excess reserves in the banking system really doesn't make commercial bank loans more likely. Non-bank private entities literally have no use for Fed deposits, which is why they don't need Fed deposit accounts. Non-bank private entities are really only concerned with their bank deposits and physical cash, and that physical cash (most of it anyway) originates from bank deposits (e.g. ATMs).

**Note that both coins and paper bills (notes) are minted by Treasury, but the Fed only pays Treasury the cost of production for the paper bills whereas they pay face value for the coins.

***Coins (as opposed to paper notes) are actually assets of the Fed after being purchased from Treasury at face value (but before being sold to banks): kind of a historical oddity, and I think the basis of the Trillion Dollar Coin idea for skirting the debt limit. The vast bulk of bank reserves (paper notes and electronic reserves) don't show up on the Fed's balance sheet until they are sold to banks, and then they appear as a liability to the Fed (in the case of electronic reserves they of course don't even exist until they are credited to banks!). Of course when coins are sold to banks, they are removed  from the Fed's balance sheet (i.e. they are erased as Fed assets).

Help Requested!

If you're like me, concepts stay fuzzy until you make a concrete example out of of them. There are still a couple of important MR concepts that I'm having a hard time understanding fully. One has to do with the "Corporate Profits Breakdown" chart on this post and the related Kalacki equations:

http://pragcap.com/chart-of-the-day-corporate-profits-vs-the-sp-500

Cullen has an explanation in his "Understanding the Modern Monetary System" paper/posts, but there's also this more detailed explanation here by JKH:

http://monetaryrealism.com/saving-stockflow-consistency-and-kalecki/

Right there at the top of JKH's post he also covers the other concept I'm still having a hard time with (because I still can't fully think of simple concrete examples for it), and that's the S = I + (S - I) and related formulas/identities.

I'm wondering if it's possible to create a tiny-Macro world to illustrate these concepts on balance sheets, similar to the way I've done it elsewhere in this blog. In particular, I'd love to be able to populate a world with a minimal set of entities with which to illustrate each concept. Perhaps that's a fools errand and I should quit now!! I don't know.

What I'm imagining I'd need is (at least one of each):

1. central bank (CB)
2. Treasury (gov)
3. domestic commercial bank
4. person
5. foreign CB with an account at the CB
6. foreign commercial bank with an account at the CB
7. foreign person
8. Some kind of physical asset(s)? (not sure if I need this)

Ideally I'd like to start off with everyone's balance sheets absolutely clear, except perhaps for ownership of some physical asset (perhaps a bull and a cow that can reproduce and create more), by a person say. Perhaps a bank loan could kick start the economy into gear. The goal would be to demonstrate in a concrete way on each entity's balance sheet, all the concepts/flows that JKH and Cullen cover in their posts on this subject. In particular I mean:

GDP = C + I + G + (X – M)

GDP = C + S + T

S = HS + FS

Business gross profit = undistributed gross profit + distributed profit

Business gross profit
= I – (HS + (T – G) + (M – X)) + DIV       
= investment – household saving – government saving – foreign saving + dividends

I'd also like to demonstrate, in a concrete way, exactly how JKH explains where MMT goes wrong (read JKH's entire post to see what I'm talking about). My level of understanding at this point isn't great enough that I could confidently dig in and start to populate balance sheets to demonstrate these concepts! To see how I struggle sometimes, take a look at this post which I put together after multiple comments exchanged with commentator "Joe in Accounting" here at pragcap:

http://brown-blog-5.blogspot.com/2013/03/banking-example-7-calculating-capital.html

Here's the thread:

http://pragcap.com/towards-a-mostly-cashless-monetary-system/comment-page-1#comment-141344

Anyway, the point of this post is to let people know about this project and ask for your help! I guess I could start with exactly which kind and quantity of entities I'd need to populate my world with. Or perhaps somebody has already done exactly what I'm looking for and I can save myself a whole lot of trouble by just looking at what they've already done!

Any ideas?? Please contact me or leave a comment. Thanks!

Banking Example #7: Calculating Capital vs Equity

The purpose of this example is to demonstrate how to calculate bank capital in various ways vs equity. This post was inspired by a comment thread with Joe in Accounting at pragcap. My basic concern was to distinguish capital from equity. Joe also distinguished capital from a "simple accounting perspective" vs capital from a "regulatory perspective." I'll refer to these two broad categories as "accounting capital" and "regulatory capital" respectively. I also made use of Wikipedia articles, such as this one on Tier 2 capital. As a warning, I really need Joe in Accounting or somebody else who knows about these concepts to review what I've done here! But as is the usual case with this blog, I'll just pretend I know what I'm talking about and hope to be corrected later.

Setup: one bank (A) and one person x. Bank A's balance sheet:

Bank A

Assets	Liabilities
$120 reserves	$75 subordinated debt bond sold w/ maturity < 1 year
------------------	$45 bond sold w/ maturity > 1 year
$100 loan to x	$90 deposit for x
Negative Equity	Equity
------------------	$10

Regulatory Capital:

The Tier 1 capital in this case is the same as equity (shareholder's equity or owner's equity: see here for more details), which is simply:

Tier 1 capital = assets - liabilities = $220 - $210 = $10

After calculating Tier 1, it's possible to calculate Tier 2 capital. The subordinated debt in the liabilities column is the only component in this case. Tier 2 capital is limited to be no more than 100% of Tier 1 capital (I'm also assuming it can't be less than 0). Thus we have:

Tier 2 capital = max(0, min(subordinated debt, Tier 1 capital)) = max($0, min($75, $10)) = $10

Thus the combined Tier 1 + Tier 2 capital is $20. Now for purposes of calculating a regulatory capital adequacy ratio (CAR) we have:

CAR = (Tier 1 capital + Tier 2 capital) / (sum of risk weighted assets) = $20 / ($120*0 + $100*1) = 20%

Here I've assumed the loan to person x is high risk and thus weighted by the maximum weight, 1, while the reserves are by definition of no risk, and thus weighted by the lowest weight, 0. Had the loan been a mortgage, for example, it may have had a weight of 0.5 instead, which would have improved (increased) the CAR.

Accounting Capital:

One kind of accounting capital we might wish to calculate is working capital. This represents funds available in the near term with which to acquire other investments. It's defined as:

working capital = current assets - current liabilities

See the Wikipedia article for definitions. We'll assume the loan to x can be liquidated in less than a year for its book value, which means that

current assets = $120 reserves + $100 loan to x = $220

Current liabilities, however, does not include the $45 bond with a maturity greater than 1 year, thus we have:

current liabilities = $75 subordinated debt + $90 deposit = $165

and thus

working capital = $220 - $165 = $55

Observations:

In summary then, we have:

Bank A

Name	Value
Equity	$10
Tier 1 capital	$10
Tier 2 capital	$10
Tier 1 + Tier 2 capital	$20
Working capital	$55

You might find it strange (as I did) that calculating Tier 2 regulatory capital involved ADDING a liability, whereas the usual way of calculating capital or equity is to follow a formula like

capital or equity = set of assets - set of liabilities

with liabilities SUBTRACTED from the other term. But this isn't so strange if you consider that Tier 2 is calculated after Tier 1 and that it's limited in value to 100% of Tier 1, and that the usual purpose in calculating Tier 2 is to add it to Tier 1 to form the numerator of the CAR. Thus in forming this sum we don't want to double count the assets. In other words, the assets on the balance sheet have already been folded into Tier 1, and in fact the liabilities that contribute to Tier 2 have already been subtracted in the Tier 1 calculation. Thus adding some fraction of certain liabilities back in (up to 100%, depending on how large the "raw" calculation of Tier 2 is compared to Tier 1, i.e. the figure we get before limiting it), really just cancels that fraction of the liabilities out of what was already calculated in Tier 1, to form an expanded measure of capital. In other words:

Tier 1 capital = assets - liabilities

Tier 1 + Tier 2 capital = assets - subset of liabilities

I've oversimplified a bit here, and actually "set of" should precede all occurrences of either "assets" or "liabilities" .. only they are different sets on the two lines. For example, Tier 2 can also include other assets (it just doesn't in this case).

This concept can be further clarified by introducing an alternative method of calculating working capital. In this case we will simply add the qualifying liabilities to the equity (assuming all the assets are current assets, which they are in this case). The qualifying liability here is still just the long term $45 bond. Thus we could write:

working capital = equity + long term liabilities = $10 + $45 = $55

The long term liabilities have already been subtracted in the calculation of equity, thus what we are really doing here is simply cancelling them out in the calculation of working capital. In other words, rather than adding them you could imagine that we are simply NOT subtracting them. Here's another simple example: say bank B starts out with a clear balance sheet:

Bank B

Assets	Liabilities
$0	$0

Clearly all equity and capital calculations result in $0. Now suppose it sells a long term bond (maturity > 1 year):

Bank B

Assets	Liabilities
$100 reserves	$100 bond sold w/ maturity > 1 year

The equity is still $0, but if we note that current assets = assets, we have:

working capital = assets - current liabilities = $100 - $0 = $100

Or, alternatively:

working capital = equity + long term liabilities = $0 + $100 = $100

Now if bank B were to spend all its reserves on donuts (while the regulators weren't looking) and pass them out to the public for free in an unsuccessful attempt to attract customers (the working capital in this case was put into a terrible investment!), we'd have:

Bank B

Assets	Liabilities
$0	$100 bond sold w/ maturity > 1 year
Negative Equity	Equity
$100	-------------------------------------

Now we calculate:

working capital = equity + long term liabilities = -$100 + $100 = $0

The point is that we're not getting something for nothing here. If there are no assets at all, then we'd expect the working capital to be no greater than $0 (and our expectations are met). We're adding in qualifying liabilities in the calculation, but only because for the definition of capital at hand, we've already subtracted them in the equity term. So in a sense, rather than adding them (the qualifying liabilities), we're just NOT subtracting them.

Banking Example #1.2: Loan & Deposit Transfer (w/ Colors!)

Example of a loan and deposit transfer. Coloring of cells inspired by commenter Geoff at pragcap.com (an attempt to make it more clear, by matching assets with their related liabilities across balance sheets). Otherwise this is exactly the same as Example #1. Each color represents a financial entity: loan, deposit, etc. Cells with the same color represent two views of the same entity, one from the creditor's viewpoint (left hand column) and one from the debtor's viewpoint (right hand column). Example #10 demonstrates how these different financial entities are interrelated but have a degree of independence from one another.

Setup: one central bank (CB), two commercial banks A and B, and one person x. No reserve requirements or capital requirements and everyone's balance sheet initially clear (empty).

Initial balance sheets (for CB, A, B, and x):

CB, A, B, x

Assets	Liabilities
$0	$0

Balance sheets after x takes a $100 loan from A:

Bank A

Assets	Liabilities
$100 loan to x	$100 deposit for x

Person x

Assets	Liabilities
$100 deposit at A	$100 borrowing from A

Balance sheets after x transfers deposit from Bank A to Bank B:

Central Bank

Assets	Liabilities
$100 reserve overdraft for A	$100 reserve deposit for B

Bank A

Assets	Liabilities
$100 loan to x	$100 overdraft at CB

Bank B

Assets	Liabilities
$100 reserves	$100 deposit for x

Person x

Assets	Liabilities
$100 deposit at B	$100 borrowing from A

Balance sheet after Bank A borrows $100 of reserves from Bank B and repays CB the overdraft amount by the end of the day (note: Bank A could have borrowed from any other bank, the money markets, the Central Bank's discount window or by attracting transfer deposits, but I've chosen to show the case where it borrows from Bank B):

Central Bank

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$100 loan to x	$100 reserve borrowings from B

Bank B

Assets	Liabilities
$100 loan of reserves to A	$100 deposit for x

Person x

Assets	Liabilities
$100 deposit at B	$100 borrowing from A

Note that at the end, the central bank's balance sheet is again clear, yet there are $100 of reserves on loan to A from B. To see a similar case where the deposit transfer is accomplished with a purchase instead, see Example 1.1.

I recommend this writeup on the monetary system by Cullen Roche for more information. Also, I must credit this article. Also, this site animates balance sheets, and has an especially good macro page with consolidated balance sheets.  Look at this to see this same example with reserve requirements, and here to see it with both reserve and capital requirements.

List of Ways Reserves Leave the Banking System

See this post for a simplified list of where reserves can go (ignoring the distinction between inside and outside the banking system).

First of all, we need to define what is meant by reserves in the banking system. In the US this commonly includes reserves in the private banks' central bank (Federal Reserve Bank or just "Fed") reserve accounts (these are the only accounts on which the Fed pays "interest on reserves" (IOR)). It also includes "vault cash" which is physical currency/cash (paper bills and coins) stored at the private banks. It does not include the Federal government's Fed reserve account (the Treasury General Account (TGA)). It also does not include anything the Fed itself holds as an asset: reserves are never a Fed asset; they are always a Fed liability. All Fed reserve accounts are electronic. The Fed is an independent hybrid public/private institution, and thus not strictly part of the government. Of course the Treasury Department (or just "Treasury") is part of the federal government. We also need to consider other government agency Fed accounts (government sponsored enterprises, or GSEs).

Here, then, is the list of ways in which reserves leave the private banking system:

1. When entities pay taxes/tariffs/fees/fines (and those payments are transferred to the TGA or GSE Fed accounts)
2. When Treasury or GSEs auction bonds (and the proceeds are transferred to the TGA or GSE Fed accounts)
3. When private non-banks withdraw paper bills and coins (physical cash or currency) from their private bank deposits
4. When private banks repay Fed reserve loans or overdrafts (principal and interest)
5. When foreign central banks or institutions (e.g. the IMF) receive funds in their Fed reserve accounts
6. When the Fed/Treasury/GSEs sell assets (typically Treas. bonds, but also could include foreign currency, TARP assets, etc.) to private entities, for example during Fed Open Market Sales (OMSs)

First of all notice that "loaning out reserves to private non-banks" is not on the list. That's an incorrect way to think of reserves. Only chartered banks, Treasury, and certain GSEs, foreign central banks, and institutions (IMF, World Bank, etc.) can hold Fed reserve deposit accounts. Individuals, non-bank businesses, and most organizations cannot hold Fed reserve accounts. Reserves can be loaned by individual banks to other banks, and they can be transferred between banks to back/clear purchases or payments between private entities including when the purchasing entities are the banks themselves (e.g. to pay bank employee salaries, or to buy office supplies for the bank), but these events do not cause reserves to leave the banking system as a whole.

I've not made a distinction between excess reserves (ER) and required reserves (RR) in the above, although you can take the list to apply to ERs since RRs are of course required (by regulation), and thus are only absent (below their required levels) for brief periods of time. There are other ways in which, in aggregate (i.e. taking all banks as a whole), excess reserves can be converted to required reserves (and thus in that sense "leave the banking system"), but those are not covered by the above list since it makes no distinction between reserve types. Of course there are other ways reserves can leave, come into, or be converted from excess to required status by individual banks (as opposed to the banks in aggregate).

Of the six entries on the list, the first two and the interest component of the fourth* are typically reversed when the Federal government spends money. The third is reversed when currency is re-deposited in private banks by private entities. The principal component of the fourth is reversed by the Fed loaning out reserves (note that reserve loans are typically made on the inter-bank market, but the Fed stands ready as a lender of last resort, thus the bulk of Fed reserve loans are typically repaid in short order when replacement reserves are obtained from other entities). The fifth is reversed when funds exit these foreign central banks and institutions (note that foreign owned private banks are part of the banking system). The sixth is reversed by Fed Open Market Purchases (OMPs). Together OMSs and OMPs constitute Fed Open Market Operations (OMOs). So in terms of reserves permanently leaving the banking system, this only happens when the Federal government starts accumulating money in the TGA (i.e. running a surplus), when currency is permanently kept, destroyed or lost by the private sector, when Fed reserve loans are repaid, or when OMSs are not eventually reversed by OMPs. Government surpluses have historically been rare and comparatively little currency is kept, destroyed or lost by the private sector. Net "permanent" Fed reserve loans are really only made to the aggregate banking system to support reserve requirements (typically ~10% of bank demand/checking deposit liabilities). This leaves OMSs as the main way in which reserves leave the banking system most of the time. Conversely, OMPs are the main way reserves are injected into the banking system most of the time. OMPs are how "Quantitative Easing" (QE) is accomplished. Treasury deficit spending does NOT inject reserves into the banking system. Instead it injects net financial assets (i.e. Treasury bonds) into private hands, and at the same time takes the proceeds from the bond auctions and spends them back into the private sector. Thus, in a sense (though not literally), the Treasury obtains and spends private bank created money (inside money) when it deficit spends. This is not literally true, since the Treasury spends from it's Fed deposit (the TGA), but this deposit was funded largely through the private sector: either by taxes or bond auctions. Non-banks purchasing Treasury debt or paying taxes use inside money to do so. In the case of private non-banks, funding the TGA is the mirror image of spending from the TGA: funding involves the elimination of a bank deposit and the simultaneous transfer of outside money from the banks (which may have to borrow from the Fed for this purpose) into the TGA. Spending involves the transfer of outside money from the TGA to the banks, and the simultaneous creation of bank deposits for the non-bank payees. Of course what counts as money can be debated. In our system, bank deposits have a very high degree of moneyness.

Assuming that Treasury immediately spends its Fed deposit (i.e. the TGA is immediately emptied: not a terrible assumption with deficit spending), then the sum of non-bank held commercial bank deposits (& cash) is equal to the sum of private bank loans and the Treasury debt held by the Fed & banks. Why is this? (henceforth in this discussion I'll use "bank deposits" to mean "bank deposits & cash" for simplicity, since cash is mostly just withdrawn deposits). For starters, since "loans create deposits" we'd expect to be able to express the bank deposits of non-banks in terms of loans (loans to Treasury being called "Treasury debt" here). But why doesn't this statement include all Treasury debt? To see why consider the following example: assume we start off with everyone's balance sheets clear (zeros for assets and liabilities), and then the Fed & banks acquire $X in Treasuries. This results in $X in bank deposits when Treasury spends. Now these deposits can be traded by the non-banks for the Treasuries and back again.... in any amount up to $X. Thus bank deposits can vary between $0 and $X under this trade. Now assume that bank loans in the amount of $Y are made to non-banks. Now non-bank deposits can vary between $Y and $(X+Y) depending on the amount of Treasuries traded with the Fed & banks (the maximum still being $X). At this point we've accounted for, in terms of debt, all existing non-bank bank deposits. If the non-banks now use any part of these deposits to purchase Treasuries from Treasury, those deposits will be returned to them (in aggregate) once Treasury spends and thus the aggregate bank deposits will not change. Since this process can be repeated an indefinite number of times (assuming Treasury continues to auction bonds and spends all the proceeds each time), the total amount of T-bonds acquired by the non-banks in this manner can total $Z, where Z can be any positive value, without changing the aggregate non-bank bank deposits. If the Fed & banks purchase some of these new Treasuries from the non-banks, the non-bank bank deposits will increase accordingly. Thus the total amount of bank deposits held by the non-banks can vary between $Y and $(X+Y+Z) depending on how many Treasuries are traded with the Fed & banks. Only to the extent that the Fed & banks hold a part of the $(X+Z) in existing Treasuries, are non-bank bank deposits elevated above $Y, and thus the only case in which these bank deposits total the full $(X+Y+Z) is when the Fed & banks purchase all existing Treasury debt.

Note that I'm simplifying a bit here by glossing over the process by which Treasury Tax and Loan (TT&L) accounts are created as an intermediate step before transferring funds to the TGA -- this transfer being necessary before the funds can be spent by Treasury.

These JKH and Ramanan comments at monetaryrealism.com provides further insight

*Note that almost all the interest paid to the Fed for its reserve loans is remitted by the Fed to Treasury, and thus will almost certainly be spent again into the private sector.

Banking Example #3.2: Capital Requirements (Simplified Stock Issuance)

Example loan and deposit transfer with both reserve and capital regulatory requirements. Required capital is partly raised by a stock issuance and partly by retained earnings (from a loan origination fee). Example #3 is a simpler variation on this without the stock sale (i.e. capital requirements are met entirely through retained earnings). Example 3.1 is a more complicated example documenting the balance sheets associated with a stock investor as well.

Setup: one central bank (CB), two commercial banks A and B and one person (x). Reserve requirements are 10% of deposits, capital requirements are 10% combined Tier 1 and  Tier 2. This example was inspired by this John Carney article at CNBC.  

On the bank balance sheets which follow, loans and the capital requirements they induce will be colored green, while deposits and the reserve requirements they induce will be colored red.  Assume starting out that that any preexisting entries on the CB's balance sheet (e.g. having to do with stock investors owning $5 in the first place*) are summarized in the cells "preexisting assets" and "preexisting liabilities." You can assume, of course, that the CB's balance sheet is initially in balance, i.e.: preexisting assets = preexisting liabilities

Note that all balance sheets are shown only on the first and last steps. Only balance sheets which change are shown on the intermediate steps.


Initial balance sheets for CB, A, B and x:

A, B, x

Assets	Liabilities
$0	$0

CB

Assets	Liabilities
preexisting assets	preexisting liabilities

Balance sheet after Bank A sells $5 of stock to unnamed investors:

CB

Assets	Liabilities
preexisting assets	preexisting liabilities - $5
-----------------	$5 reserve deposit for A

Bank A

Assets	Liabilities
$5 reserves at CB	$0
Negative Equity	Equity
------------------	$5

Balance sheets after x takes a $100 loan from bank A (note: I've chosen to show that bank A meets half its capital requirements by charging a $5 origination fee to x for the loan [please read Carney above for other ways to find capital and reserves], which it keeps as retained earnings. This lowers x's deposit by $5, and thus lowers the reserve requirements from $10 to $9.50. I've chosen to show bank A borrowing $4.50 of this reserve requirement from the CB):

CB

Assets	Liabilities
preexisting assets	preexisting liabilities - $5
$4.50 reserve loan to A	$9.50 reserve deposit for A

Bank A

Assets	Liabilities
$100 loan to x	$95 deposit for x
$9.50 required reserves	$4.50 reserve borrowing from CB
Negative Equity	Equity
------------------------	$10 required capital

Person x

Assets	Liabilities
$95 deposit at A	$100 borrowing from A
Negative Equity	Equity
$5	------------------------

Balance sheets after x transfers deposit from Bank A to Bank B:

Central Bank

Assets	Liabilities
preexisting assets	preexisting liabilities - $5
$4.50 reserve loan to A	$95 reserve deposit for B
$85.50 reserve overdraft for A	--------------------------

Bank A

Assets	Liabilities
$100 loan to x	$85.50 reserve overdraft at CB
--------------------	$4.50 reserve borrowing from CB
Negative Equity	Equity
--------------------	$10 required capital

Bank B

Assets	Liabilities
$95 reserves ($9.50 required)	$95 deposit for x

Person x

Assets	Liabilities
$95 deposit at B	$100 borrowing from A
Negative Equity	Equity
$5	------------------------

Balance sheets after Bank A borrows $85.50 of reserves from Bank B and repays CB overdraft by the end of the day (note: Bank A could have borrowed from any other bank, the money markets or the CB's discount window or by attracting new transfer deposits, but I've chosen to show the case where it borrows from Bank B):

CB

Assets	Liabilities
preexisting assets	preexisting liabilities - $5
$4.50 reserve loan to A	$9.50 reserve deposit for B

Bank A

Assets	Liabilities
$100 loan to x	$85.50 reserve borrowing from B
--------------------	$4.50 reserve borrowing from CB
Negative Equity	Equity
--------------------	$10 required capital

Bank B

Assets	Liabilities
$9.50 required reserves	$95 deposit for x
$85.50 loan of reserves to A	-----------------

Person x

Assets	Liabilities
$95 deposit at B	$100 borrowing from A
Negative Equity	Equity
$5	------------------------

Note: as Carney states, these are simplified reserve and capital requirements. As in the Wikipedia article I link to above, what I'm really doing here for the capital requirements is calculating a capital adequacy ratio (CAR) as the ratio of capital to the sum of risk weighted assets. The loan on bank A's balance sheet is risky, thus it's weighted by the maximum weight 1 (lower risk assets get smaller weights, which increases the CAR, all else being equal). I'm also taking equity = capital. Thus the CAR in this case is $10 equity / $100 loan = 0.10 = 10% which just meets the CAR requirement (10% or greater is satisfactory).

Joe in Accounting helped me with this example, but I still need to run it by him to make sure it's correct.

*To see a related example documenting the balance sheet changes associated with a stock investor as well (rather than having unnamed investors) see Example 3.1.