Wednesday, August 21, 2013

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.

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