How Government Borrowing Pushes Bond Yields

A government that spends more than it collects has to borrow, and borrowing means competing for the same pool of saving every other borrower is drawing on. More borrowing against an unchanged pool raises what borrowers have to offer to get funds. How far it rises depends on whether the pool is growing, who else is asking, and who is lending.

A government that spends more than it receives must borrow the shortfall, and the shortfall has a name and a size, set out where the deficits are compared. Where the borrowed money goes, and how narrowing the gap acts on the rest of the economy, is set out where government spending and consolidation are covered. A second lever reaches the same market from the other direction, worked by the central bank rather than the finance ministry, and is set out under monetary policy. How a price forms at all when buyers and sellers meet was settled at the very start of this subject.

One joining move remains, and the move is smaller than it sounds. The borrowing a government has to do goes inside the market for funds, where a price forms the way a price forms anywhere else. Once the borrowing is in there, the direction falls out on its own, and so does the reason nobody can state the size in advance.

Every place and figure below sits inside the Republic of Sankhya, an invented country used across these notes so that arithmetic can be followed end to end without borrowing a real number from anywhere. Sankhya's government spends Rs 4,00,000 crore in the year and collects Rs 3,00,000 crore, so its fiscal deficitThe gap between everything a government spends in a year and everything it receives that is not itself borrowing. It is the amount that has to be raised from lenders. How it is measured, and how it differs from the other two deficits, is covered where the deficits are compared. is Rs 1,00,000 crore, which is 5.72 per cent of its outputThe total value of everything an economy produces in a year, measured in the money of the day. It is the yardstick almost every government figure is compared against, and it is covered where the output measure is built. of Rs 17,47,200 crore. Rs 1,00,000 crore is the amount that has to be found, and it is the only figure the account below needs from the government's books.

What is being supplied and what is being demanded here?

Start with what is easy to get wrong: what kind of market this even is. The first sequence of these notes taught how a price forms when people who want something meet people who have it, and that is the whole engine here. Borrowing is buying, lending is selling, and the thing being traded is the use of somebody else's money for a period. A borrower is a buyer of funds. A saver is a seller of funds. Nothing else needs to be true for the rest of this guide to work.

A wedding in an ordinary street makes the same point. Six households on that street are saving through the year, putting money aside they do not intend to spend yet. Four other households are trying to raise money now: one is buying a small shop, one is paying a college fee, one is replacing a delivery van, one is putting on the wedding. The savers have the money and would part with it for a period on the right terms. The borrowers want it now and will pay something for it. There is a going rate on that street, and it is set by how many savers there are against how many borrowers, exactly as the price of onions in the market at the end of the street is set by how many sacks arrived against how many people came to buy.

Scale that street up to a country and the picture does not change shape. On the selling side sits the pool of lendable savingAll the money in an economy that has been set aside rather than spent, and is available to be lent out for a period. Households, businesses sitting on cash, insurers and pension funds and, in an open economy, savers abroad.: households putting part of a salary aside, businesses holding cash they have not yet used, insurers and pension funds holding money against promises that fall due later, and savers in other countries willing to send money in. On the buying side sits everyone who needs money now and does not have it: a household buying a house, a small business buying a machine, a large company building a plant, a state authority laying a road. The Sankhya government is one more name on that buying side, and the market does not treat it as a special case merely because it is a government.

The price of funds in Sankhya is measured on a scale of its own. The scale reads 100 points before the borrowing arrives, and every move is read against that. The unit is points rather than per cent. Put a per cent on the price of funds and it starts to look like something quoted on a real instrument.

Why does a government arrive as an unusual buyer of funds?

Now put the Sankhya government on the buying side and watch how it behaves differently from everybody standing next to it. A company that wants Rs 500 crore for a new plant is watching the price of funds the whole time it is deciding. If funds get dear enough, the plant stops making sense and the company simply does not come to the market this year. A household looking at a home loan behaves the same way, only faster: the loan gets expensive, the purchase is postponed, the demand for funds quietly disappears. An ordinary borrower is always free to not borrow, so an ordinary borrower's demand for funds falls away as the price of funds rises.

The Sankhya government does not have that freedom in the year in question. Its spending of Rs 4,00,000 crore has already been authorisedApproved in advance by the legislature, which votes on what the government may spend before the spending happens. The document that carries the approval and the timetable it runs on are covered where the Union Budget is covered., its receipts of Rs 3,00,000 crore did not cover it, and the gap of Rs 1,00,000 crore has to be found. Salaries are due. Interest of Rs 90,000 crore on money borrowed in earlier years is due, and that one is not postponable at all. A road half built is worth less than either a finished road or an unstarted one. So the government comes to the market needing Rs 1,00,000 crore, and if funds turn out to be dear, it comes anyway and pays what it has to.

A market with a buyer in it whose demand barely falls when the price rises prices differently from a market without one, and that is the whole of what a government adds here. Everyone else in the room can walk away. The government cannot walk away, or at least not inside the year, and everyone else in the room knows it. The household version is a wedding whose date is fixed and whose hall is booked: the flowers can be argued about, but the caterer is going to be paid this month at whatever this month's price turns out to be.

Why does government borrowing act on the price of borrowing?

Here is the direction, stated once and plainly. The Sankhya government arrives at the market for funds needing Rs 1,00,000 crore that was not being asked for before. The pool of saving has not changed. Every other borrower is still there, wanting what it wanted. There is now more demand for funds against the same supply of them, and a market answers that in exactly one way. More borrowing against an unchanged pool of saving means a higher price for funds, and that direction is the claim.

The direction is easier to believe once the mechanics are visible, so follow what has to happen for the money to be found at all. Nobody prints an extra Rs 1,00,000 crore of saving to order. The Rs 1,00,000 crore has to come out of the pool that exists, and it comes from two places at once. Some savers who were not going to lend this year are drawn in by a better price, so the pool itself gets a little bigger. And some borrowers who were going to borrow decide the price has moved past what their plan can carry, so they step aside and leave their share behind. Both of those things only happen if the price of funds rises. The rise in the price is what does both of them.

In Sankhya's case, with the pool as it stands, the price of funds settles 10.00 points higher, at 110.00 points against 100.00 before. Savers bring Rs 40,000 crore more than they were going to. Private borrowers take Rs 60,000 crore less than they were going to. The extra saving and the abandoned borrowing add to Rs 1,00,000 crore, precisely what the government needed, and there is no third place the money could have come from.

Two assumptions are doing work in that picture, and both are assumed rather than measured. The first is that every point the price of funds rises brings Rs 4,000 crore more saving into the market. The second is that every point it rises takes Rs 6,000 crore of private borrowing back out. Change either number and the arithmetic changes with it. The direction does not change. A direction can be established from the mechanism alone, and a size cannot.

Why does the size of the borrowing matter and not only its purpose?

People argue hard about what a government is borrowing for, and the argument is a real one. Money borrowed to build a road leaves a road behind. Money borrowed to pay this year's salaries and this year's interest leaves nothing behind that a later year can use. Sankhya's own Rs 1,00,000 crore splits into capital spendingSpending that buys or builds something lasting, a road, a bridge, a building, rather than paying for this year's running. How it is separated from revenue spending is covered where government expenditure is covered. of Rs 70,000 crore and a remaining Rs 30,000 crore, and that remaining Rs 30,000 crore is the revenue deficit exactly. Note what that is: subtracting capital spending from the borrowing has to leave the revenue deficit whenever there are no non-debt capital receiptsMoney a government takes in from selling something it holds or from a loan being repaid to it, rather than from borrowing. Where it sits in the account is covered where government revenue is covered., so it is an identity rather than a finding, and it can never come out any other way. The identity is still worth reading precisely. Rs 30,000 crore of the borrowing funded consumption rather than assets.

The split lives in the government's accounts and not in the demand for funds, so the market for funds cannot see any of it. A lender being asked for Rs 1,00,000 crore is being asked for Rs 1,00,000 crore. There is no arrangement by which the road-building portion draws money out of the pool more gently than the salary-paying portion. Both are the same rupees leaving the same pool, and both squeeze the same private borrowers standing behind them in the queue.

None of that is an argument that purpose does not matter. Purpose decides what the country has afterwards, and what next year's account looks like, and whether the borrowing was worth doing. Purpose decides nothing at all about what happens to the price of funds this year. Purpose and size answer two different questions, and reading an answer to one as an answer to the other is where a lot of confident commentary goes wrong.

What decides how much a given amount of borrowing moves the price?

Now the part that gets left out, and it is the part that makes the difference between understanding this and being able to use it. The direction is fixed. A price is settled by both sides and the government is only one of them, so nothing on the government's side of the transaction fixes the distance. The same rupee of borrowing can move the price of funds a great deal or hardly at all, and what decides which is entirely outside the borrowing figure.

Three things do most of the deciding. The first is whether the pool of lendable saving is growing. A pool that grew by nearly as much as the government is taking has already found most of the money without anybody having to be outbid. The second is whether private borrowers are asking at the same time. In a strong stretch of the cycleThe run of good and weak stretches an economy goes through, in which output and hiring speed up and slow down. Where it comes from and how it is read is covered under the business cycle. businesses are queueing for funds and the government is one more elbow in a crowded room; in a weak stretch they have shelved their plans, and the room is half empty. The third is who is lending. A pool that includes insurers and pension funds with money that must be placed somewhere for a long period behaves quite differently from one that depends on savers who can take their money elsewhere the moment they like the look of somewhere else.

Two more things sit alongside and matter just as much, and neither is settled here. There is a separate lever, the policy rateThe rate the central bank sets, which acts on the price of borrowing across the economy from a different direction and on its own timetable. It is covered under monetary policy., being worked by the central bank on its own timetable and acting on the same market. And there is what lenders think about being paid back and about what money will be worth by the time they are. Both of those move the price of funds without any borrowing figure changing at all. Any observed move is therefore the sum of several things and not one of them.

What happens when the same borrowing meets three different markets?

The three cases below are worth slowing down for. Take Sankhya's Rs 1,00,000 crore, hold it completely fixed, and place it three times into a market whose other side is doing three different things. The borrowing figure is identical in all three. The figure is the published fiscal deficit of Rs 1,00,000 crore, 5.72 per cent of an output of Rs 17,47,200 crore, and it does not move.

One borrowing figure produced three different moves, and the largest of them is ten times the smallest. Look at what survived and what did not. The direction survived. In all three an extra Rs 1,00,000 crore was asked of a pool that had to find it, and in all three the price of funds ended higher than it began. The size did not survive at all. Anyone who had been told that a deficit of this size moves the price of funds by so much would have been right once and wrong twice, and would have had no way of knowing which of the three they were living through until afterwards.

Follow the money in each case and the differences stop being mysterious. In case one, savers brought Rs 40,000 crore more and private borrowers gave up Rs 60,000 crore, and it took a 10.00 point rise to persuade both. In case two, savers had already brought Rs 94,000 crore more, so private borrowers only had to give up Rs 6,000 crore and barely had to be persuaded at all. In case three, savers brought Rs 24,000 crore more while private borrowers gave up Rs 76,000 crore, most of which they had already decided to give up for reasons of their own. In every case the two contributions add to exactly Rs 1,00,000 crore, the amount that had to be found, and the price move is only the size of the persuasion required.

Why can borrowing rise while the price of funds barely moves?

Case two is the one that unsettles people, so it is worth naming what happened there in plain words. The Sankhya government borrowed the full Rs 1,00,000 crore. The price of funds moved 1.00 point. Somebody reading only the headline would see a large borrowing figure sitting beside a market that shrugged, and would conclude that something is wrong with the mechanism.

Nothing is wrong with it. Savers had brought Rs 90,000 crore more to the market than the year before, so nine tenths of what the government needed was already sitting there waiting to be lent. Only the last Rs 6,000 crore had to be taken off a private borrower, and taking Rs 6,000 crore off a private borrower does not require much persuasion. Borrowing rising while the price of funds barely moves is not a contradiction, it is what an ordinary period looks like when the other side of the market was growing at the same time.

A reader who expects borrowing and the price of funds to move together does not just miss this case, they misread it. Such a reader sees a period where borrowing was high and the price of funds was calm, and concludes that borrowing must not act on the price of funds after all. Then they see the next period, where the same borrowing meets a pool that did not grow, and the price of funds jumps, and they have no explanation for the difference except that something changed in the government's behaviour. Nothing changed in the government's behaviour. The side of the market the reader was not looking at is the side that changed.

There is a stronger version of the same case, and the honest thing is to state it rather than leave it out. If savers had brought more than the government needed, say Rs 1,50,000 crore against a requirement of Rs 1,00,000 crore, the price of funds would have ended the year lower than it began. The borrowing was still pulling upward the whole time. The upward pull was simply outweighed. A mechanism outweighed is not a mechanism failing. Borrowing is one of several things acting on the same price at once, which is the ordinary condition of every number in economics, and a single figure never settles anything on its own. The case appears in the panel above under the last of the presets.

What does an analyst actually do with a direction alone?

A direction without a size sounds like half an answer, and a reader is entitled to ask what anybody is meant to do with it. The honest reply is that a direction changes the question worth asking. Changing the question is more useful than it sounds, and it is most of what careful work in this subject consists of.

Somebody covering government finances for a lender or a research desk does not read the borrowing figure and stop. The next move is to go looking for the other side. How much is the pool of saving expected to grow this year, and where does that estimate come from. Are businesses investing and standing in the queue for funds at the same moment, or have they gone quiet. Who is expected to lend: long term holders who have to place money somewhere, or savers who can go elsewhere. Is the central bank pulling in the same direction as the government or the opposite one. The borrowing figure by itself is one side of a market and settles nothing until the other side has been looked at. An analyst therefore treats the figure as the beginning of the work rather than the end of it.

A household version of the same discipline is easier to feel. News that a large employer in a town is about to hire two hundred people settles nothing about how far rents will rise. The next question is how many flats are empty. Two hundred new tenants against fifty empty flats is one story and against six hundred empty flats is another, and the number of new tenants is identical in both. The direction was never in doubt. The size was never in the hiring announcement.

Where does this account stop and fixed income begin?

The title names bond yields, and the distance between a price of funds and a bond yield is worth stating exactly.

A direction inside a market for funds is what the account so far has established. A government that must borrow arrives on the buying side of that market, and its arrival raises what borrowers have to offer, by an amount that depends on what the selling side and the rest of the buying side were doing at the same time. Government borrowing and the price of borrowing are connected in exactly that way, and about direction the answer is complete.

How a bond is priced, what a yield is as an arithmetic object, and how a price and a yield move against each other are all still open. All three belong to fixed income, a subject in its own right rather than a footnote to this one. The arithmetic of yields gestured at in a sentence or two would be taught badly, and a reader would come away thinking it had been learned.

The difference between the two is the difference between knowing that more buyers in a market push a price up and knowing how to price the specific instrument being traded. Both are worth having. Only the first one is here. The second belongs to fixed income, where the price of a bond, what a yield measures and the relationship between the two are covered properly.

The Republic of Sankhya, its government account and its pool of lendable saving are invented.
Educational material. Not advice on any investment, tax, budget or market position.