tl;dr: this whole thing looks very, very sketchy
- RRP = reverse repurchase facility
- FI = financial institution
- This is not financial advice
- Peers, please review! I am posting this to get insight and improvements from the community. My understanding is limited, and I’d like to expand it.
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To simplify our understanding of RRP operations, let’s ignore the confusing mechanics  and just follow the money trail. The mechanics are (deliberately?) confusing because not only “repurchase” is an obfuscation of “a loan”, not only it is a “reverse” repurchase – meaning “investment” as the reverse of a loan? But also if one amount becomes negative the whole thing is flipped on its head, and also if the narrator expresses these ideas from the point of view of the counterparty, then it’s flipped on its head again. 
The simplification I propose is to simply say, who’s paying in this transaction? And from their point of view, what are they borrowing, and why?
The FED is paying 4% on RRP transactions, so the FED is the purchaser/borrower. What does the FED borrow in these transactions, cash or treasuries? It borrows cash. So the FED borrows cash from the system (from all eligible institutions), and pays cash to do so. Now, let’s try to figure out why.
There is an imbalance of cash and treasuries in the system. As you can see, around 2008 the FED’s (read: the USA government’s) balance sheet exploded, allowed trash toxic waste onto the balance sheet, and has been growing the balance sheet (read: sinking into insolvency) ever since.
An intermediary(?) outcome of QE is that the FED “printed” too much money. There is too much cash and not enough treasuries in the system, causing an **imbalance**. The RRP seeks to address this imbalance. This imbalance threatens to devalue cash (the dollar), since there is too much of it, increased supply, value of money goes down. The FED is counter-acting this by borrowing cash from the system, decreasing the supply of cash, and increasing the price of cash (dollars).
Does QE increase, or decrease inflation? (And please, do respond with criticisms. I’m only learning all of this now, for the last 2 years, and I definitely need peer review.) According to my first simplification (which seems incorrect, as I discuss later), QE **lowers** inflation. If you consider strictly supply and demand of treasuries, and treasury yield (inverse of treasury price) as loosely corresponding to inflation. Then, QE is **purchases** of treasuries, which drives the price (of treasuries) up, which drives yields (= inflation) down.
Why is the above interpretation wrong? Because we know, that the FED finances these purchases by “printing” “money”, which increases the supply of “money”, decreasing its value. Which is exactly what inflation is: loss of purchasing power of the dollar. So now you have two competing forces (peers! is this right?): treasury yields go down, **and** they go up.
In fact, for the latter of the two: does the excess of printed money in the system cause yields to go up? If you have way too much money, you’d put it somewhere, maybe even in treasuries. But this relationship is not simple or straightforward, because treasuries isn’t the only investment instrument that exists. In fact, if a FI’s believe the inflation to be e.g. 10%, they would not invest in treasuries unless the treasuries are cheap enough to give them 10% return. They would put money in riskier assets instead, or in real estate or whatever. So yields must go up (treasury prices must go down) given inflationary economic outlook.
So you have too much money in the system, at the same time as noone wants to put that money into treasuries. I think RRP is the facility to reduce this excess money in the system.
Unfortunately, the FED decided to pay FI’s 4% to park their cash – and the payment injects more cash in the system. It appears that the “solution” exacerbates the problem in the long term.
-  https://www.newyorkfed.org/markets/rrp_faq
-  https://en.wikipedia.org/wiki/Repurchase_agreement#Reverse_repo