Banking Example #11.2: Macro Balance Sheets: Even More Details

Update 1 2013.08.26: Changed the role of variable "G": it no longer contributes to public's money stock.
Update 2 2013.08.26: Changed the role of variable "Mg": it no longer contributes to the public's money stock. (more below)
Update 3 2013.08.31: Removed M, Mb, Mf, Mg and replaced with Lb, Lf, Lg as in Ex #11.1

This post is just a more detailed version of Example #11.1 which in turn was a more detailed example of Example #11. Please refer to those prior posts for explanations of the assumptions made and the independent variables I adopt here from them. Here I'm adding three new independent variables to describe the non-Tsy governmental sector (intra-governmental). This includes agencies like Social Security that have their own tax revenue stream and government sponsored enterprises (GSEs) like Fannie, Freddie and Ginnie Mae. I'm lumping these all on one balance sheet that I call "Non-Tsy Gov." The three new variables are: G = intra-governmental held Tsy debt (this is a very large percentage of Tsy debt in the USA), Ug = unspent intra-governmental Fed balances and Lg = intra-governmental held MBS. Note that T, unlike in Example #11, now explicitly includes the component from the non-Tsy government sector, but still excludes the foreign sector. However, overall this post is still not really complete:

1. I have to find out if my non-Tsy Gov sector sells its own debt (I'm assuming no for now)
2. Ditto for 2. but equity (I think this is true, but I'm not taking this into account: i.e. I think the public can hold shares of Ginnie Mae, etc, but I'm not sure!)
3. Just generally check it over and make sure there are no errors. I'm still finding errors in the much simpler Example #11 (I haven't yet for #11.1, but it hasn't been up that long!)

In light of the incompleteness of this post, please don't take it as the gospel truth! Also, if you see where I'm making an error (mathematical or otherwise) PLEASE let me know! Thanks! (I'm putting this out there early in the hopes I get some good feedback).

BTW, I know this is getting more and more ridiculously complicated, but I hope to puff it all up, and then carve it back down again, just leaving in place what I think are the really important pieces: for example maybe it makes sense (somewhere down the road) to aggregate the foreign sector and the intra-governmental sectors together. After I "puff it up" I want to find some good realistic numbers to substitute in and then take a look at what we've got. 

UPDATES: As of Aug. 31, 2013, I've made an important correction to the following tables: This correction has to do with how G & Lg affect the bank reserve and public's bank deposits expressions: previously I erroneously had them entering into these expressions, but it no longer does. Re: G: This is because G really just represents an imbalance in spending between the intra-gov (non-Tsy gov) agencies (which have their own revenue streams (e.g. SS)) and the Tsy. Imagine we draw a line around both Tsy and non-Tsy gov and look at it as one entity: if non-Tsy gov takes in $X in taxes, and Tsy takes in $0, but non-Tsy gov spends $X on Tsy-bonds and Tsy spends $X, then the public sees $X into the government and $X back out. This does not contribute to the public's money stock. The resultant $X in Tsy debt now held by non-Tsy gov simply represents the fact that non-Tsy gov collected the revenue and Tsy spent it. Now suppose that in the next reporting period the tables are turned and Tsy collects $X in revenue and the non-Tsy gov collects $0, but non-Tsy spends $X. But where did non-Tsy get the $X? Tsy will end up spending their $X paying the principal back on the Tsy debt purchased by non-Tsy in the previous period, and rather than using the proceeds to buy more Tsy debt, non-Tsy spends it (supposing the next period is enough time for that debt to mature). Again, the public sees $X in and $X out. The fact that the accumulated intra-gov Tsy debt disappears has no effect on the public's stock of money or equity. Re: Lg, the argument is similar to that of G, but in this case you can think of it like this: The public first loses Lg in tax money to the non-Tsy gov (which results in the banks needing to borrow Lg in Fed deposits from the CB to send to the non-Tsy gov). The non-Tsy gov exchanges its Lg in Fed deposits for Lg of MBS from the banks. The banks use the Lg in Fed deposits received in the exchange to pay off the loan of reserves from the CB.

Proceeding directly to the variables and balance sheets we have:

Independent Variables

Name	Range	Description
T	0 < T	Total Tsy debt outstanding**
B	0 < B < T-F-G	Tsy debt held by banks
F	0 < F < T-B-G	Tsy debt held by the Central Bank
L	0 < L	Bank loans & mortgages to public
C	0 < C < Lb+Lf+B+F-Ut-Ug-D	Cash in circulation in public
Ut	0 < Ut < Lb+Lf+B+F-C-Ug-D	Unspent Tsy funds (TGA balance)*
D	D < Lb+Lf+B+F-C-Ut-Ug	Bank income net of expenditures
Lb	0 < Lb < L-Lf-Lg	Bank held loans to public
Lf	0 < Lf < L-Lb-Lg	Fed held loans to public (MBS)
G	0 < G < T-B-F	Tsy debt held intra-governmentally
Ug	0 < Ug < Lb+Lf+B+F-C-Ut-D	Unspent non-Tsy government funds
Lg	0 < Lg < L-Lb-Lf	Inter-governmental held MBS

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

Tsy

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

Non-Tsy Gov

Assets	Liabilities
$Ug Fed deposit	-----------------
$G t-debt	-----------------
$Lg MBS	-----------------
Total Assets	Total Liabilities
$(G+Lg+Ug)	$0
Negative Equity	Equity
------------------	$(G+Lg+Ug)

CB

Assets	Liabilities
$F t-debt	$(F+Lf-C-Ut-Ug) reserves (Fed deposit for banks)
$Lf MBS	$(Ut+Ug) other Fed deposits
--------------	$C cash
Total Assets	Total Liabilities
$(F+Lf)	$(F+Lf)

Banks

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

Public

Assets	Liabilities
$(Lb+Lf+B+F-C-Ut-Ug-D) deposits	$L borrowing
$(T-B-F-G) t-debt	---------------------
$C cash	---------------------
$(L-Lb-Lf-Lg) loans & MBS	---------------------
Total Assets	Total Liabilities
$(T+L-Lg-G-Ut-Ug-D)	$L
Negative Equity	Equity
--------------------------------------	$(T-Lg-G-Ut-Ug-D)

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

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

CB

Assets	Liabilities
$F t-debt	$(Ut+Ug) Fed deposits
$(C+Ut+Ug-Lf-F) reserve loans to banks	$C cash
$Lf MBS	------------------------
Total Assets	Total Liabilities
$(C+Ut+Ug)	$(C+Ut+Ug)

Banks

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

Again note the unique way G (non-Tsy gov held Tsy debt) is treated here in relation to F and B. G does not contribute to the public's money stock or to bank reserves as do the others. It does contribute in a similar way to the Tsy debt held by the public. See the paragraph in italics at the top for an explanation for why G does not contribute to the public's money stock. The implication of this is that my previous examples, #11 and #11.1 were justified in ignoring the non-Tsy governmental holding of Tsy debt PROVIDED we adjust T (the total Tsy debt issued) in this cases by first subtracting off the intra-governmental (non-Tsy) held debt. A similar argument can be made for foreign held debt I think (still have to work out the details here!). Fed held Tsy debt must be counted in the total as before. So for instance if Fed, bank and public held Tsy debt only amount to 36% of all Tsy debt issued, then we should set T = to 36% of all Tsy debt issued in Examples #11 and #11.1. For this example we can include the intragovernmental held debt, but we still must exclude the foreign held debt. 

Other planned additions to these balance sheets (that I'll save for future posts) include foreign sector (foreign central banks, international organizations (e.g. IMF), etc.), and required reserve ratios.

So in the spirit of simplifying these overly complex looking balance sheets and trying to uncover the most interesting point to be made about them, I'll do the same here as at the bottom of the Example #11 post, and show the public's balance sheet under simplified circumstances: Lb = L and D = Ug = Ut = 0:

Public (simplified)

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

Now it's very clear how G contributes (or doesn't contribute) to the public's equity and money stock, specifically, just as in Example #11, the expression for the public's money stock is still:

public's money stock = L + B + F

with no dependence on G. The equity, however, is modified here (as T-G instead of T) to represent that T now includes this non-Tsy government sector, which must be subtracted out. Note again that T (like in Examples #11 and #11.1) still does not include the foreign sector, which I'm still ignoring.

You might wonder "But does this have to do with non-Tsy gov buying directly from Tsy? What happens if they buy Tsy-debt from the public?" Well, that would imply that Ug > 0 (i.e. that unspent non-Tsy gov funds existed) which violates my simplifying assumptions. But if we go back and let Ug > 0, then you can see that it (Ug) directly subtracts from the public's money stock (in the more complex public balance sheet presented earlier), and thus trading Ug for G  does increase the public's money stock, but that's taken care of by the decreasing Ug term, and so G still doesn't enter into it.

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 Ug. Also 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 non-Tsy gov, the Fed, the banks & the public. Specifically excluded here are foreign holdings. 

Below is a PREVIEW of a coming post (perhaps just this one redone). In it I'm proposing to wrap both intra-governmental and foreign up in one big new entity called "X-org" (I'm putting it here in case somebody has some feedback for me about my plans!):

So what I'm proposing to do here is to create a new "X-org" balance sheet representing the aggregated effects of both the non-Tsy intra-governmental and the foreign sectors. This new balance sheet will thus incorporate Federal worker retirement funds, Social Security (SS), GSEs (Fannie, Freddie, and Ginnie Mae), and all other such government agencies AS WELL AS all foreign governments, central banks, international organizations (both legal and criminal: e.g. the IMF and Mexican drug cartels), etc. The reason for this is:

1. To try to keep the number of balance sheets and variables from getting out of control
2. Aggregated together all such organizations have one super-set of common traits

Looking at point 2 above in more detail, such an aggregate organization will be able to:

1. Hold US Tsy debt
2. Hold Fed deposits
3. Hold MBS
4. Hold cash (still assuming only reserve notes here: not coins or US notes)
5. Sell its own obligations: debt, currency, central-bank liabilities, bonds, whatever.

Perhaps this is a bad idea. I guess I'll just jump right in and find out! The new variables required will be Tx = X-org held Tsy debt, Ux = unspent X-org held Fed deposits, Lx = X-org held MBS, Cx = X-org held cash, X = X-org generated obligations (central bank liabilities, bonds, notes etc). Now since X is meant to describe the total amount of this obligation/debt/note issued by X-org, now I'll unfortunately need more "X" variables to describe the amount of X held by each of the other players. I'll assume Tsy can't hold any, but the rest can. Thus Xf = central bank held X notes and Xb = bank held X notes. Thus X-Xf-Xb represents the public held X notes. Here's how the balance sheet would look for entity X-org:

X-org

Assets	Liabilities
$Ux CB deposit	$X debt
$Tx T-debt	----------------------
$Lx loans & MBS	----------------------
$Cx cash	----------------------
Total Assets	Total Liabilities
$(Ux+Tx+Lx+Cx)	$X
Negative Equity	Equity
---------------------	$(Ux+Tx+Lx+Cx-X)