Banking Example #6: QE: CB Holds Gov Debt to Maturity

This example looks at what happens when the central bank (CB) purchases Treasury bonds from the public and holds them to maturity. For just the purchase see Example 4.

Setup: one central bank (CB), one government Treasury Department (Treasury), one commercial bank (A), and one person (x). No reserve or capital requirements. All balance sheets are initially clear (empty). This post was inspired by a question posed in a comment here. This post doesn't really answer that question directly, but reflects a thought experiment I did at the time, wherein I wondered what would happen if the CB kept purchasing and holding Treasury bonds to maturity.

Initial balance sheets :

CB, Treasury, A, x

Assets	Liabilities
$0	$0

Balance sheets after x takes a 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 buys a Treasury bond from Treasury (I'm skipping the step where A experiences an overdraft at the CB when x's deposit is transferred to Treasury to clear the bond purchase, and I'm going straight to bank A borrowing funds to cover the overdraft, in this case from the CB):

Treasury

Assets	Liabilities
$100 reserves	$100 Treasury bond held by x

CB

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

Bank A

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

Person x

Assets	Liabilities
$100 Treasury bond	$100 borrowing from A

Balance sheets after the CB purchases the Treasury bond from x:

Treasury

Assets	Liabilities
$100 reserves	$100 Treasury bond held by CB

CB

Assets	Liabilities
$100 loan of reserves to A	$100 deposit for Treasury
$100 Treasury bond	$100 deposit for A

Bank A

Assets	Liabilities
$100 loan to x	$100 reserve borrowings from CB
$100 reserves	$100 deposit for x

Person x

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

Balance sheets after Bank A repays its reserve borrowings from the CB:

Treasury

Assets	Liabilities
$100 reserves	$100 Treasury bond held by CB

CB

Assets	Liabilities
$100 Treasury bond	$100 deposit for Treasury

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 Treasury pays x for services rendered to the government:

Treasury

Assets	Liabilities
$0	$100 Treasury bond held by CB
Negative Equity	Equity
$100	--------------------------------

CB

Assets	Liabilities
$100 Treasury bond	$100 reserve deposit for A

Bank A

Assets	Liabilities
$100 loan to x	$200 deposit for x
$100 reserves	------------------

Person x

Assets	Liabilities
$200 deposit at A	$100 borrowing from A
Negative Equity	Equity
------------------	$100

Balance sheets after x repays loan to A:

Treasury

Assets	Liabilities
$0	$100 Treasury bond held by CB
Negative Equity	Equity
$100	--------------------------------

CB

Assets	Liabilities
$100 Treasury bond	$100 reserve deposit for A

Bank A

Assets	Liabilities
$100 reserves	$100 deposit for x

Person x

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

Balance sheets after Treasury sells another bond to x to cover its upcoming principal payment to the CB:

Treasury

Assets	Liabilities
$100 reserves	$100 Treasury bond held by CB
------------------	$100 Treasury bond held by x
Negative Equity	Equity
$100	--------------------------------

CB

Assets	Liabilities
$100 Treasury bond	$100 reserve deposit for Treasury

Bank A

Assets	Liabilities
$0	$0

Person x

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

Balance sheets after the first Treasury bond matures and Treasury repays the principal to the CB:

Treasury

Assets	Liabilities
$0	$100 Treasury bond held by x
Negative Equity	Equity
$100	------------------------------

CB

Assets	Liabilities
$0	$0

Bank A

Assets	Liabilities
$0	$0

Person x

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

Balance sheet after CB buys Treasury bond from person x:

Treasury

Assets	Liabilities
$0	$100 Treasury bond held by CB
Negative Equity	Equity
$100	------------------------------

CB

Assets	Liabilities
$100 Treasury bond	$100 reserve deposit for A

Bank A

Assets	Liabilities
$100 reserves	$100 deposit for x

Person x

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

Now at this point, if the government wants to continue deficit spending, it must now sell another Treasury bond (e.g. to x), and continue this process. As this cycle of events continues, x's equity will continue to climb by $100 each time and Treasury's equity will continue to decrease by $100 each time (with the CB's and Bank A's equity staying at $0). Person x will not need to take a loan the next time around since he has $100 of deposits with which to purchase the next bond. Of course the government can also tax Person x to reduce the amount of deficit spending it must engage in to keep this process going. If the CB were to purchase every Treasury bond in this manner, the effect would look similar to "monetizing the debt." Ultimately CB and A are performing as intermediaries. In reality the CB only purchases a small fraction of the outstanding Treasury bonds under Quantitative Easing (QE) operations, for example. Plus, it's ultimately up to x whether or not to sell the bonds, since the CB does not directly purchase bonds from Treasury.

This example is over simplified and has many shortcomings. Interest, taxes, fees, and changing bond prices are not covered. These would be significant over the course of a bond's issuance to maturity. Also, Bank A would not likely borrow from the CB to repay its reserve overdraft, but instead would most likely borrow from another bank. Also, x would not likely take a loan out to purchase a Treasury bond, since it would probably experience a negative spread on the two interest rates if it did so. However, someone else may take out such a loan to hire x for his services, which would provide x with the funds to purchase a Treasury bond: thus you can think of x and A as stand-ins for the aggregate non-bank and bank private sectors.