Banking Example #11: Possible Macro Balance Sheets

In this post I am trying to capture a large set of possible balance sheets here in a simplified world consisting of just four basic entities. I'm making many simplifications (of course), but I do think it gives some insight into exactly what are some possibilities via placing simple formulas in each balance sheet cell rather than concrete numbers like I usually do.

This world consists of just four entities, two of which represent aggregates: The Treasury (Tsy), the central bank (CB), the commercial banking sector (banks), and the non-bank private sector (public). The public represents all non-bank businesses, private organizations, and individuals making up the private sector economy. This world does NOT include foreign exchange, government sponsored enterprises (GSEs), or international organizations holding CB deposits (e.g. the international monetary fund (IMF), or foreign central banks). It also does not include shadow banking or concepts such as "rehypothecation." The basic assumptions are as follows:

1. Banks don't hold inventories of vault cash
2. No reserve or capital requirements on the banks
3. No coins or US notes (reserve notes are assumed as the only cash)

Now assume that the Tsy has sold $T of Tsy debt (t-debt) to the public, banks and Fed (Tsy debt not sold to one of these three entities should be excluded here: see Example #11.2 for further discussion), the CB has purchased $F of this debt, the banks have purchased another $B of it, and the public has purchased the remaining $(T-F-B) of it. Also assume that the public has taken out $L in bank loans and that they've withdrawn $C in bank deposits in the form of cash (physical bank notes). Ut is the unspent balance in the Tsy Fed deposit (the TGA). D represents the difference between the public's outstanding loan balance and the public's bank deposits + cash: i.e. it is the net total of payments to the banks by the public for interest, points, fees and service charges net of interest, employee salaries, shareholder dividends, and other payments by the banks to the public (electric bills, rent, office supplies, etc). I break my example balance sheets up into two cases. In the first, the amount of cash (C) is less than or equal to the amount of t-debt held by the CB (F) minus the unspent Tsy balance (Ut). In this case excess reserves (ER) are > 0 (the quantitative easing (QE) case). In the other case, C+Ut is greater than F but less than or equal to L+B+F-D (the amount of bank deposits held by the public if there was no cash in circulation). This is the ER = 0 or non-QE case. You can also assume that all balance sheets started off initially clear (no assets or liabilities), and that any ordering of events was used to arrive at the following balance sheet states, including Tsy auctions, lending and buying or selling of after market t-debt by the various entities. And of course, T, F, B, L, C and Ut are all non-negative. D can be either positive or negative, but must obey D < L+B+F-C-Ut. Should further net fees to banks be paid once D = L+B+F-C-Ut, it can be assumed those are incorporated into L. Note that Ut > T is allowed* (i.e. Tsy is running a surplus) however, this is rare, and it's easier in general to assume that Tsy spends every dollar it gets and thus that Ut = 0. You might wonder here, "What about mortgages?" Well certainly the Fed can buy mortgage backed securities (MBSs) so that's important to include. Also there's a government sponsored enterprise (GSE) component and a foreign component that I'm ignoring here. All that will be addressed in a subsequent post (and part of it is already!).

Independent Variables

Name	Range	Description
T	0 < T	Total Tsy debt outstanding**
B	0 < B < T-F	Tsy debt held by banks
F	0 < F < T-B	Tsy debt held by the central bank
L	0 < L	Bank loans outstanding to public
C	0 < C < L+B+F-Ut-D	Cash in circulation in public
Ut	0 < Ut < L+B+F-C-D	Unspent Tsy funds (TGA balance)
D	D < L+B+F-C-Ut	Undistributed bank equity

Case 1: Excess Reserves: (ER > $0 or C+Ut < F)

Tsy

Assets	Liabilities
$Ut Fed deposit (TGA)	$T t-debt
Negative Equity	Equity
$(T-Ut)	-----------

CB

Assets	Liabilities
$F t-debt	$(F-C-Ut) reserves (Fed deposit for banks)
--------------	$Ut TGA (Fed deposit for Tsy)
--------------	$C cash
Total Assets	Total Liabilities
$F	$F

Banks

Assets	Liabilities
$L loans	$(L+B+F-C-Ut-D) deposits for public
$B t-debt	---------------------------------------
$(F-C-Ut) reserves	---------------------------------------
Total Assets	Total Liabilities
$(L+B+F-C-Ut)	$(L+B+F-C-Ut-D)
Negative Equity	Equity
--------------------	$D

Public

Assets	Liabilities
$(L+B+F-C-Ut-D) deposits	$L borrowing from banks
$(T-B-F) t-debt	--------------------------
$C cash	--------------------------
Total Assets	Total Liabilities
$(T+L-Ut-D)	$L
Negative Equity	Equity
-----------------------------	$(T-Ut-D)

Case 2:  No Excess Reserves: (ER = $0 or F < C+Ut < L+B+F-D)

Note: Only the CB and Banks balance sheets change for this case:

CB

Assets	Liabilities
$F t-debt	$Ut TGA (Fed deposit for Tsy)
$(Ut+C-F) reserve loans to banks	$C cash
Total Assets	Total Liabilities
$(Ut+C)	$(Ut+C)

Banks

Assets	Liabilities
$L loans to public	$(L+B+F-C-Ut-D) deposits for public
$B t-debt	$(Ut+C-F) reserve borrowings
Total Assets	Total Liabilities
$(L+B)	$(L+B-D)
Negative Equity	Equity
------------------	$D

Notice that the only change between Case 1 and Case 2 is on the CB and Banks' balance sheets: the Tsy and public balance sheets were unchanged. Also notice that in both cases the CB has no equity, while the Tsy has negative equity of $(T-Ut) and the public and banks have a combined positive equity of $(T-Ut).

For simplicity, in the rest of  the discussion below assume that Tsy spends every dollar it gets (not an outlandish assumption!) immediately and thus the unspent Tsy balance is zero (i.e. Ut = 0). This is not required but makes it easier. Also assume that D = 0 (i.e. all the banks' equity has been paid out, e.g. distributed to shareholder, etc.), again for simplicity.

For a given level of independent variables T and L, the public's money (bank deposits and cash) can vary linearly between L and L+B+F while the public's t-debt simultaneously varies linearly between T and T-B-F, depending on the amount of t-debt allocated between the CB and banks on one hand, and the public on the other.

How can this be used? Here's an example: A simple demonstration that the statement "banks lend out excess reserves" (ER) is at bit misleading. While true that cash advances do occur (C and L increasing simultaneously) I demonstrate here that what's important is that bank lending can lead to an increase in the stock of the public's money, but it has nothing to do with reserves, so the only important part of that sentence is "banks lend," the "reserves" part doesn't have any macro significance. Since my assumption is reserve requirements = 0%, all bank reserves are excess: meaning we're under "Case 1" with ER > 0. From the sheets under Case 1:

banks reserves = F - C = ER

So what happens to the non-bank private sector's (the "public's") stock of money (bank deposits + cash) if:

1. F goes down: This results in the public's stock of money going down, $ for $.
2. C goes up: This results in the public's stock of money staying the same.

All else (i.e. other independent variables) being equal (unchanged), in both cases. Thus whatever we twiddle here to make ER go down, the result is that the public's stock of money either goes down or stays the same. It's certainly true that both C and L can go up simultaneously, thus both increasing the stock of money and decreasing the stock of excess reserves, however think about how that can be accomplished: By literally ONLY loaning out cash (or more accurately immediately exchanging for cash the bank deposits which result from lending). Cash advances are a minor component of overall lending.

Reader Geoff has coded up a simplified version (w/o Ut or D) on a spreadsheet which I imported into MS Excel Web App for an interactive version below. It's still a ways from this very cool interactive tool but it's not too bad! Try it out by modifying the contents of the green cells at the top. You can also download a version using the Excel Web App black tool bar along the bottom of the spreadsheet (green Excel icon). Note: I don't do a range check on the inputs to make sure they're valid so if you see something odd, like a negative number anywhere except for Tsy's equity, or an odd looking plot, you probably are violating a range limitation on an input (see the above table of independent variables for valid ranges). If not, let me know! I may have a bug.



Finally note that if we set Ut = D = 0, and just focus on the five main independent variables, the public balance sheet looks like this:

Public (simplified)

Assets	Liabilities
$(L+B+F-C) deposits	$L borrowing from banks
$(T-B-F) t-debt	-------------------------------
$C cash	-------------------------------
Total Assets	Total Liabilities
$(T+L)	$L
Negative Equity	Equity
-----------------------	$T

With the public's equity in this case exactly equal to the Tsy's debt. It's also clear what the stock of public money is most reliant upon: private sector borrowing from banks (L), and institutional Tsy debt purchases (B and F). Cash (C) washes out as it simply represents bank deposits exchanged for paper notes: notes which the Fed provides in any case. If they didn't, our ATMs would run dry (which you may have noticed, they don't). All of this misses a HUGE part of what constitutes public investment and savings, for example real assets (such as real-estate). This post touches on some of what's missing from the above analysis in this regard. Simplifying further, but ignoring the distinction between deposits and cash (i.e. setting C = 0), we have:

Public (more simplified)

Assets	Liabilities
$(L+B+F) deposits	$L borrowing from banks
$(T-B-F) t-debt	-------------------------------
Total Assets	Total Liabilities
$(T+L)	$L
Negative Equity	Equity
-----------------------	$T

Notes:

* Ut > T means that the resulting "Negative Equity" for Tsy in both cases (which is normally represented with a positive number on the left here) would actually take on a negative value. Normally when that happens I null out "Negative Equity" and put positive equity on the right under "Equity" but it doesn't really matter too much: the balance sheets will balance with either method (and I kind of had to choose one since I can't have a balance with entries under both!). A similar note applies to D, but in this case I've nominally entered a positive expression on the "Equity" side of the banks' balance sheet. 

** T is total Tsy debt in this world, which includes that owned by the Fed, the banks, and the public. Specifically excluded here are foreign and intra-governmental holdings (such as Social Security, etc.)