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)

 

Banking Example #11.1: Macro Balance Sheets: More Details

This post is just a more detailed version of Example #11. Please refer to that prior post for explanations of the assumptions made and the independent variables I adopt here from that example.

Example #11 was already complicated enough for a single post. This example will skip most of the verbiage and fancy interactive balance sheets and just concentrate on the "enhanced" balance sheets and accompanying independent variables. I will add details in increments, so initially I'll just start with adding mortgage backed securities (MBS). There's several ways this can be done, and I've chosen one of them here. I've added two new variables here: Lf = mortgage debt held by the central bank, and Lb = mortgage debt & loans held by the banks. The additions to the table of independent variables (brought over from Example #11) made to accommodate these new variables have been highlighted in yellow. 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	Tsy debt held by banks
F	0 < F < T-B	Tsy debt held by the Central Bank
L	0 < L	bank loans & mortgages to public
C	0 < C < Lb+Lf+B+F-Ut-D	Cash in circulation in public
Ut	0 < Ut < Lb+Lf+B+F-C-D	Unspent Tsy funds (TGA balance)*
D	D < Lb+Lf+B+F-C-Ut	Bank income net of expenditures
Mb	0 < Lb < L-Lf	Bank held loans to public
Mf	0 < Lf < L-Mb	Fed held loans to public (MBS)

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

Tsy

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

CB

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

Banks

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

Public

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

Case 2:  No Excess Reserves: (ER = $0 or F+Lf < C+Ut < Lb+Lf+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-Lf) reserve loans to banks	$C cash
$Lf loans	--------------------------------
Total Assets	Total Liabilities
$(Ut+C)	$(Ut+C)

Banks

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

Other planned additions to these balance sheets include government sponsored enterprises (GSEs) and other government Tsy debt and Fed deposit holders (e.g. Fannie, Freddie, and Social Security), and a foreign sector (foreign central banks, international organizations (e.g. IMF), etc.).

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.

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.)

Market Monetarists: Please Explain!

In recent discussions with David Beckworth about a recent post of his, I've become confused as to what the Market Monetarist (MMist) position really is on some key issues. Commentator "Jared" brought David's post to my attention when he commented about it at pragcap. Since then, the discussion has moved from David's site to pragcap and back again (under a different post). Jared's latest on this has been very clarifying.

Basically the discussion has boiled down to the following: David talks about leaving the interest on reserves (IOR) rate at 0.25% as the rate on short term Treasury debt rises, as a way to increase inflation and nominal GDP (NGDP) and all the things that MMist love. He claims this can be done while committing to a permanent increase in the stock of "base money" meaning that the Fed keeps the stock of excess reserves (ERs) above zero (and doesn't let them decrease). In fact not only CAN it be done, he claims that's the way to do it. Or at least I thought that's what he was claiming until his latest comment. He also brings up cash, but I think Jared effectively dismissed that pretty quickly. Plus David responded to me with one of his previous posts (wherein he claims he did a better job of explaining himself) where he explicitly considers the case of a "Cashless Society." Actually, when pressed, I've found that all the MMist I regularly read claim that cash isn't really important. That includes Nick Rowe, David Glasner, Scott Sumner, and now David Beckworth. Even some hyperinflationists have told me that cash isn't important, even though their arguments seemed to imply that it was. (I'll try to provide a few more links here when I get the chance: I think I saved links to all the occurrences where MMist told me cash wasn't important). Although one hyperinflationist ("bart") took a slightly different tact when he explained that my argument was "made null" by not taking into account "rehypothecation" and "collateralization" (presumably of the ER). He lost me there.

Meanwhile, the discussion with David has now gotten into the realm of the common MMist claim that the endogeneity of inside money really only holds over a short term (six week) basis between Fed meetings (or BoC in Nick Rowe's case). Rowe also touched on that here, and so has Scott Sumner and David Glasner. So have I for that matter, though I was less endorsing the view than explaining it. Jared admits some difficulty with this concept, but ultimately concludes that inside money is ALWAYS endogenous. I don't know if I can follow him there yet. I'm still undecided. However, I'd love to get back to the original issue: how can short term rates rise above the IOR rate when ER > 0? And if they can't, then what's the point of increasing the "base money" stock through central bank (CB) asset purchases (i.e. Quantitative Easing (QE))? Would it have to do with the rest of the yield curve? Is it just for psychological purposes?

Also, I suppose we could go the Japanese route and veer off into "non-traditional" asset purchases by the CB, but then is that really still "monetary policy" or have we entered the realm of "fiscal policy?" I think I know where each side comes down on that question, but it seems a little beside the point, since folks like Sumner have said that it's highly unlikely that these kinds of asset purchases would ever be necessary, while Glasner laid out a specific scheme where the kinds of assets purchased didn't really matter. I don't doubt that if the Fed starting buying non-traditional assets (Cullen Roche often mentions "bags of dirt") they could definitely raise the inflation rate. (I know... I owe you more links).

By all means, read Jared's argument(s). They are very good. I perhaps have muddled the issue by building on Beckworth's cashless society concept to conceptually simplify my argument. My assumptions are:

1. No cash (paper reserve notes or coins)

2. No reserve requirements (reserve requirement = 0%)

3. Only a single commercial bank (or just think of all commercial banks aggregated together)

In such a system "base money" = electronic Fed deposits at the bank (i.e. reserves, or excess reserves, since none are required). Since reserves can only go three places there's limited items our one commercial bank can buy with them. Essentially it boils down to Tsy debt from Tsy auctions. If the Fed were selling (which it's not... according to David's earlier comments, it's committed to keeping stocks of base money elevated: i.e. ER > 0) they could buy Tsy debt or mortgage backed securities (MBS) from them too (in which case the base money would be destroyed). Now when the bank spends on Tsy debt (or when private sector entities pay taxes) the reserves sent to the Treasury General Account (TGA: Treasury's Fed deposit, from which it can spend) end up in the bank again when Treasury spends into the real economy. So our bank can spend base money on Tsy debt at Tsy auctions, but that base money will end up right back on the bank's balance sheet shortly thereafter. It's only a temporary way to get rid of it. That is, unless Tsy runs a surplus (which they're not).

Everything else that the bank buys it does so by crediting the bank deposits of entities in the private sector. This includes any goods or services the bank uses (electric bill, office supplies, etc), employee salaries, shareholder dividends, interest to depositors, Tsy debt held in the private sector, or any other financial assets (bonds, stocks, etc.), or new loans (you can view new loans as the bank buying loan agreements from the borrowers). Crediting bank deposits means creating inside money ex-nihilo.

I think it's pretty clear that in such a world, whenever short term Tsy debt comes up for auction, and the amount that's being auctioned is less than the stock of ER, that the bank(s) will bid the price up and thus the yield down to the IOR rate. If there's any differential, the banks won't hesitate to buy it all. If I'm wrong about that, what am I missing? Could it be that expectations of higher rates are so strong that the bank is not willing to risk a decline in principal even on very short term debt? Could that be possible?

Now perhaps my simplifying assumptions go to far. If so, which ones, and why? I'm asking for help here in understanding. My simplifying assumptions are not essential (Jared does an excellent job arguing this same position w/o resorting to them). I only made them in an attempt to make the problem more clear w/o significantly affecting the macro picture. But perhaps they are not justified. Either case, I think it would be instructive (to me anyway) to know exactly where I've gone wrong here and why, if indeed I have.

Getting back to Beckworth's position, I thought that Jared clearly summed up the dilemma of deciphering exactly where David stands, by pointing this out:

"...our discussion began with this quote from Friedman, ““Oh well, we’ve got the interest rate down to zero; what more can we do?” It’s very simple. They can buy long-term government securities, and they can keep buying them and providing high-powered money until the high powered money starts getting the economy in an expansion.” This certainly sounds like a causal (and temporal) story running from CB asset purchases (injections of high-power money) to economic expansion. But it seems as if you’re now saying that the central bank does not really need to conduct asset purchases to increase the monetary base, it just needs to credibly commit to a permanent increase in the monetary base, which could FOLLOW the inside money creation. Is your view different from Friedman’s" 

Update: Jared and JP Koning chime in on the thread. I especially liked this from Jared:

"If we cut through the jargon, by "different degree of policy accommodation to changes in demand for bank reserves," you mean the Fed will raise or lower the rate at which it provides reserves to private banks, right?" 

Update 2: Sumner makes an amazing statement:

"In a sensible system the base money is endogenous. You set the NGDP target, and the public tells you how much base money they want to hold. I’m all for that."

Banking Example #10: Balance Between Money & Debt

This example is meant to illustrate inside money creation, destruction, and the relationship between that and the creation and destruction of debt. It demonstrates these ideas through loan/deposit creation, principal & interest payments, and bank payments to the non-bank private sector via crediting bank deposits. It was inspired by the first answer to this question.

Setup:  One commercial bank (Bank A) and one person (Person x). No reserve or capital requirements and the bank.

 1. Initial balance sheets (balance sheets are clear, and thus equity = $0 for both parties):

Bank A, Person x

Assets	Liabilities
$0	$0

2. Person x takes a loan for $100 from Bank A as in Example #1.2. Notice that both parties still have $0 equity. The inside money (bank deposits) are equal to the debt in the system. It's important to keep in mind that like in the first step of Example #1.2, there are two financial entities created here, each seen from two vantage points: the loan, and the deposit. The colors highlight this fact: each color corresponds to a different entity: the yellow cells are two views of the loan, while the green cells are two views of the deposit. Views on the right hand side are from the point of view of a debtor, and views on the left hand column are from the point of view of a creditor: so Bank A and Person x are both debtor and creditor to each other. The two financial entities (loan & deposit) happen to start off with equal values in this example, but they are independent from each other (or rather they are related, but have a degree of independence) and thus their values can change with respect to one another depending on what happens next:

Bank A

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

Person x

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

3. As per the loan agreement, Bank A charges Person x $15 for the 1st payment: $10 interest and $5 principal. Person x pays it. The principal payment destroys $5 of debt and $5 of inside money. The interest payment destroys $10 of inside money without affecting the debt. The interest payment upsets the balance between debt and inside money. This imbalance is equal to the equity of Bank A (and also to the negative equity of Person x).

Bank A

Assets	Liabilities
$95 loan to x	$85 deposit for x
Negative Equity	Equity
-----------------------	$10

Person x

Assets	Liabilities
$85 deposit at A	$95 borrowing from A
Negative Equity	Equity
$10	------------------------

4. Now Bank A pays Person x $10 for services that Person x has performed for the bank. This has no effect on the debt, but it creates $10 of inside money and it also happens to restore the balance between debt and money in the system (thus equity for both parties returns to $0).

Bank A

Assets	Liabilities
$95 loan to x	$95 deposit for x

Person x

Assets	Liabilities
$95 deposit at A	$95 borrowing from A

You can take Bank A as a stand in for the aggregate commercial banking sector. Person x can likewise be taken as a stand in for the aggregate non-bank private sector. The services that Person x performs for the bank are thus a stand in for all goods & services purchased from non-bank businesses for use by the bank(s) (e.g. office supplies, building maintenance, electric bill), bank employee salaries, bank shareholder dividends, and any interest paid by the bank to its depositors.

A common criticism of a bank created fiat money (inside money) system is that bank interest charges & fees upset the balance between debt and money in the system such that the debts to the banks can never be repaid. What this claim misses is that bank profits are redistributed back to non-banks when the banks credit deposit holders (to pay them).

If more banks were involved it would not appreciably alter this example. For example, if Person x held his deposit at another bank, then Bank A would need to transfer reserves to the other bank to pay him. The central bank may need to temporarily provide these reserves in the form of loans to Bank A, but Bank A could repay the central bank by borrowing these reserves from another source. This results in $0 net in permanent reserves needed. See Example 1 for how this works in the case of a deposit transfer (which is a related idea). Examples 1.1 and 5 may also be of interest.

If reserve requirements were non-zero, the central bank would have to create some permanent reserves as well, but only enough to match a fraction of the inside money deposits created. Ultimately this is not a terribly important detail. See Example 2 for more details.

Banking Example #9: Paying Taxes

This reader inspired example simply shows what happens when an individual pays taxes to the Federal government.

Setup: the Treasury Dept. (Tsy), the central bank (CB), a commercial bank (A) and two persons: x and y. Assume that y had owned a house which x purchased exactly as laid out in balance sheet sets 1 and 2 of Example 8. Balance sheet set 2 from that example is repeated here for convenience as our starting point (I number the initial set of sheets below "2" to emphasize this). I also color the balance sheet entries to focus on.

 2. Balance sheets after person x takes a loan from Bank A and buys person y's house with it. (the yellow colored cells are the ones to watch)

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. Assume that Person y made a profit on the sale and now owes the Federal government $10k in taxes, and then pays the tax. The resulting balance sheets look like:

Tsy

Assets	Liabilities
$10k CB deposit	$0
Negative Equity	Equity
--------------------	$10k

CB

Assets	Liabilities
$10k loan of reserves to A	$10k deposit for Tsy

Bank A

Assets	Liabilities
$100k mortgage to x	$90k deposit for y
-------------------------	$10k reserve borrowing from CB

Person x

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

Person y

Assets	Liabilities
$90k deposit at A	$0
Negative Equity	Equity
---------------------	$90k

Please excuse the extra complication of two people and a house. I could claim I did that to be consistent with my desire to have most of these examples "net to zero" meaning that if all the balance sheets are consolidated together for any one step, all the financial assets should add up to $0 equity (as long as no coins are involved). But the reality is I was just lazy and so I cut and pasted from Example 8. ;^)

Banking Example #4.1: The Two Kinds of Quantitative Easing

This post is a variation on Example #4. I've eliminated some parts and added others in an attempt to simplify, clarify and explain the two kinds of quantitative easing (QE) and the difference between them.

Setup: one Treasury Dept. (Tsy), one central bank (CB), one commercial bank (Bank A), and one person x. No reserve requirements. We start off with the Tsy having sold a $100 Tsy bond and spent the proceeds into the private economy on goods and services. This results in a net liability of $100 at the Tsy and a net asset of $100 (the Tsy bond) in the private sector, but not necessarily any bank deposits in the private sector. See Example #8 to see how this can be.

In Case 1, the Tsy bond is owned by Bank A. In Case 2, it's owned by Person x. In both cases the bond owner sells it to the CB during the QE operation. The Tsy balance sheet looks like this both prior too and after the QE operation in both cases:

Tsy

Assets	Liabilities
$0	$100 Tsy bond
Negative Equity	Equity
$100	------------------

Case 1: First kind of QE: The bank sells its Tsy bond to the CB. 

Initial balance sheets prior to the QE operation (Person x not involved: assume his balance sheet is empty):

CB

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$100 Tsy bond	$0
Negative Equity	Equity
---------------------	$100

Balance sheets after the QE operation:

CB

Assets	Liabilities
$100 Tsy bond	$100 deposit for Bank A (reserves)

Bank A

Assets	Liabilities
$100 reserves	$0
Negative Equity	Equity
---------------------	$100

Case 2: Second kind of QE: The non-bank sells its Tsy bond to the CB.

Initial balance sheets prior to the QE operation (both Bank A and Person x are involved):

CB

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$0	$0

Person x

Assets	Liabilities
$100 Tsy bond	$0
Negative Equity	Equity
---------------------	$100

Balance sheets after the QE operation:

CB

Assets	Liabilities
$100 Tsy bond	$100 deposit for Bank A (reserves)

Bank A

Assets	Liabilities
$100 reserves	$100 deposit for x

Person x

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

Notice that nobody's equity changed due to QE in either case. For a fuller discussion of this fact see the discussion at the end of Example 4. Also notice that in both cases the CB's balance sheet changed in exactly the same way.

Final observation: I think the second kind of QE (case 2) is more prevalent. Also, I'm not showing some details in this case (the exact details of how the bank acts as an agent of the CB to purchase bonds on the open market), but these details are relatively unimportant.