Where you are. Nine lessons have built the machinery: typed accounts and balanced postings (lesson 3), the bank as a balance sheet (lesson 4), reserves and deposits as two tiers held in a line-by-line mirror (lesson 5), settlement as an explicit submit-then-settle moment (lesson 7), an interbank payment squaring itself in reserves (lesson 8), and a loan writing a brand-new deposit into existence (lesson 9). Through all of it, one actor has only ever been the venue: the institution whose ledger is tier 1. This lesson makes the central bank the actor, names what it is steering toward, and shows its two levers; both turn out to be postings you already know how to write.
The most argued-about ledger in the world
One sentence goes out: the central bank will begin buying government bonds. Within the hour the arguments start, and they run for years. Printing money. Debasing the currency. Saving the economy. Inflating asset prices. Whole careers are spent on either side. Now mute the shouting and watch the institution’s hands. A desk buys bonds; a back office posts the legs; two ledgers each take one balanced posting that lesson 3’s balance check would wave through without comment. The most argued-about institution in finance runs on the same double entry as every bank in this module. This lesson is those postings, plus the question the shouting usually skips: what are the levers for?
The idea in one paragraph
The central bank does not hold tier 1 for profit; it holds it in pursuit of a mandate: stable prices and full employment; money that means next year what it means today, and an economy running near its capacity. Some jurisdictions hand their central bank both halves of that mandate, others rank stable prices first; the machinery below is identical either way. To steer toward the mandate it has two levers, and both act on reserves, the money you have been posting since lesson 5. The price lever: it publishes two standing offers, a rate at which it will always lend reserves and a rate it will always pay on reserves parked with it, and the rate at which banks lend reserves to each other overnight is thereby boxed into the corridor between the two. The quantity lever: it buys bonds and pays by minting fresh reserves, called QE, or sells bonds and destroys the reserves it is paid, called QT, changing how many reserves exist at all. Neither lever is exotic. Each is a pair of balanced postings, and you will write both before the end of this lesson.
The price lever: a corridor for the overnight rate
Lesson 8 showed you why banks watch their reserve balances hour by hour: every interbank payment drains reserves from the payer’s bank toward the payee’s. By close of business some banks hold more reserves than they need and some hold less, so a market does the obvious thing: a bank that is short borrows reserves overnight from a bank with spare, and pays interest for the privilege. That overnight interest rate is the price of reserves.
The central bank does not set that price by decree. It sets two standing offers and lets arbitrage do the work.
The ceiling. The central bank stands ready to lend reserves to any bank at a published rate. No bank will ever pay a peer more than that: borrowing dearer than the standing offer is a loss with extra steps.
The floor. The central bank pays a published rate on reserves parked with it overnight. No bank will ever lend to a peer for less: parking at the central bank earns the floor with no counterparty to chase.
Wider than the screen; scroll it sideways.
Where inside the band the rate settles depends on scarcity. When reserves are scarce, banks bid the rate up toward the ceiling. When reserves are abundant, the rate falls to the floor and stops: once every bank holds more than it could plausibly need, an extra unit just sits earning the floor rate, and nobody pays a premium to borrow what everyone has spare. Plotted, the demand for reserves slopes down and then flattens dead level at the floor:
That flat tail splits central banks into two working styles. A corridor central bank keeps reserves deliberately scarce, so the rate sits mid-band, and steers it with small adjustments to the quantity. A floor central bank floods the system with reserves until the rate sits pinned to the floor, then steers by moving the floor itself. Both styles exist, and which one a given central bank runs is largely a consequence of the second lever.
The quantity lever: QE and QT
One word first. A bond is a tradable IOU: a borrower, here the government, promises to pay on a future date, and the promise itself can be bought and sold like anything else of value. That is all this lesson needs; lesson 11 returns to the short-dated kind when it asks where money sleeps.
QE stands for quantitative easing, and the name is honest: it eases by moving a quantity, the stock of reserves, rather than a price. The central bank buys bonds from banks and pays with reserves that did not exist a moment before. QT, quantitative tightening, is the same trade run backwards: bonds go back out to the banks, and the reserves paid for them are destroyed.
Read the example’s central-bank posting once more and notice what it does not contain: a source. The 200 of reserves was not moved from anywhere; the posting minted it. Module 0’s project ended on the assertion that tier 1’s total never changes as a side effect of customers paying each other; changing it is the central bank’s own act. This posting is that act, performed. And QT is its exact inverse: the reserves come back to the central bank and are not parked, not lent onward, but unwritten; tier 1’s total falls by exactly the bond leg.
You have been living off this lever since lesson 5 without the name. World.endow, which gave alice and carol their opening balances in every exercise so far, posts the very same central-bank legs as a QE purchase: assets up, the bank’s reserve line up, fresh reserves from nowhere. The toy’s honest endowment is a tiny QE, and ledger.py’s docstring promised that lesson 10 would name the real-world operation it mirrors; this is that lesson. The one difference sits on tier 2: endow goes on to credit a customer’s deposit at the bank, while a bond bought from the bank itself leaves tier 2 untouched. Hold that difference; the gotcha below turns on it.
Why mint at all? Because the price lever runs out of road: once the overnight rate has been cut to around zero it cannot usefully go lower, and easing further means reaching for the other lever. Buying long-dated bonds bids their prices up, which pushes longer-term interest rates down; lesson 11 makes that price-and-yield see-saw concrete with a T-bill. And the reserves minted along the way are what floods the corridor: a central bank that has run years of QE operates floor-style because the flat tail of the demand curve is where QE leaves you.
Check yourself
1. A bank offers to lend reserves overnight at a rate above the ceiling. Why does it find no takers, even though no rule forbids the trade?
Because the ceiling is a standing offer, not a regulation. Any would-be borrower can get the same reserves from the central bank at the ceiling rate, so paying a peer more is a voluntary loss. The floor holds by the mirror argument: lending to a peer below the floor earns less than parking at the central bank risk-free. The corridor is arbitrage against two always-open counterparties, which is why it needs no enforcement.
2. After a long QE programme, adding or draining moderate amounts of reserves barely moves the overnight rate. What is happening on the demand curve, and how does the central bank steer from there?
The system is on the flat tail: reserves are so abundant that every bank already holds more than it needs, an extra unit simply earns the floor rate, and nobody pays a premium to borrow. Quantity changes slide along a level line. So the price lever changes form: the central bank steers by moving the floor rate itself. That is floor-style operation, and it is where large QE naturally leaves you.
3. In the exercise, QE raised total reserves by 200 while carol’s deposit sat at 100 throughout. Which tier did QE touch, and why did carol see nothing?
Tier 1 only. Alder swapped one asset for another, bonds down 200 and reserves up 200, and the central bank’s sheet grew by the mirror pair. Alder’s liabilities, which is where carol’s deposit lives, never appeared in any leg. Reserves are money only banks hold; for carol’s number to move, some tier 2 posting must name her account, and QE from a bank posts none.
4. endow() and your qe_purchase() post identical legs at the central bank. What extra leg does endow post, and what is it standing in for?
Both mint fresh reserves: central bank assets up, the bank’s reserve line up. endow then also posts on tier 2: the bank’s reserves up against a brand-new customer deposit, so a person ends up holding money. It is the toy’s honest way to give alice or carol an opening balance without pretending money predates the system: a tiny QE whose proceeds pass through to a customer’s account. qe_purchase, buying from the bank itself, stops at tier 1.
Do this
Twenty minutes, from module-01-money-at-rest. Open code/central_bank_levers.py. The setup admits one bank, Alder, endows carol with 100, and hands Alder a stylised bond book of 300, posted against equity so the sheet balances before anything happens; every number in the file is stylised, round on purpose. qt_sale ships complete and is your model, leg for leg. The one TODO(you) is qe_purchase: two postings, mirror images of qt_sale; on Alder’s ledger, bonds down and reserves up; on the central bank’s ledger, assets up and Alder’s reserve line up; end with world.assert_world() so lesson 5’s tier mirror is re-checked on the spot.
python3 code/central_bank_levers.pyRun as shipped, the starter dies on NotImplementedError. Completed, the asserts confirm that a QE of 200 raises total reserves by exactly 200 and takes Alder’s bond line to 100, and that the QT then puts every balance back where it began. The final line is exactly
reserves rose and fell exactly with the bond leg; the levers are postingsThen break it once, deliberately. Flip the sign on the bonds leg of your qe_purchase, so bonds and reserves both rise, and run again: the script dies on unbalanced posting 'QE': dAssets 400 != dLiabilities 0 + dEquity 0 before a single balance changes. The validator from lesson 3 polices the central bank exactly as it polices everyone else: minting reserves takes a balanced pair of legs or it does not happen. Restore the sign. The completed version is in solutions/central_bank_levers.py.
What you can now do. You can say what the levers are for, stable prices and full employment, and you can post both of them. The price lever: two standing offers that clamp the overnight rate into a corridor, with the rate’s resting place read straight off a reserve-demand curve that flattens at the floor. The quantity lever: QE as a bonds-for-fresh-reserves swap, QT as its leg-for-leg reverse, both ordinary balanced postings that only the central bank may write, because only the central bank may change tier 1’s total. And you can keep the tiers straight while everyone around you argues: reserves minted at tier 1 are not deposits at tier 2. Next lesson the drama stops and the housekeeping begins: where money actually sleeps at night, and why T-bills get the best bed.