How Banks Create Money Through Lending, and What Limits It

When a loan is made the borrower ends up holding a deposit that did not exist a moment earlier, and a deposit is money, so the wider measures grow through lending rather than through issue. What limits the growth is only what leaks out of each round, and in the Republic of Sankhya the larger leak is not the one most readers were taught to watch.

The four money measures, which one holds what, and why one is called the narrow measureThe smallest of the money measures: the notes and coin people are holding plus the reserves the banking system keeps at the central bank. Which measure holds which item is settled where the money measures are set out. while another sweeps in time depositsMoney placed with a bank for a fixed period, so it cannot be spent straight away without giving something up. Where it sits inside the measures is settled where the money measures are set out. are all settled already. Defining the policy rateThe single rate a central bank sets, around which the rest of very short dated borrowing and lending arranges itself. The rate itself, and how a change in it travels, are settled under monetary policy. , and tracing how a change in one travels, belong to monetary policy.

The wider measure of Sankhya money is five times the narrow one. Somebody printed the narrow one. Nobody printed the rest of it, and yet it is there, spendable, held by real people in a real economy that happens to be invented. Where did four fifths of the money supply come from?

One distinction matters before the mechanism. The account below is written at the level of the whole system: what happens to the quantity of money in the Republic of Sankhya when lending goes on. How any single institution writes down what it has done is a separate subject, genuinely interesting, and covered under accounting. The mechanism turns out to be complete without a single entry.

Every figure that follows belongs to the Republic of Sankhya, an invented economy built for these notes. Its narrow measure is Rs 3,60,000 crore, made of Rs 3,00,000 crore of currency in people's hands and Rs 60,000 crore of reserves held at its central bank. Its deposits come to Rs 15,00,000 crore. Its widest measure is Rs 18,00,000 crore.

Where does the money in the wider measures come from?

The gap is where the mechanism shows itself. In the Republic of Sankhya the narrow measure stands at Rs 3,60,000 crore and the widest measure at Rs 18,00,000 crore. The ratio is exactly 5.00. The difference in rupees is Rs 14,40,000 crore, four fifths of all the money in the country.

Now ask the awkward question. The narrow measure is issued. Notes and coin are made by somebody, reserves are created by somebody, and there is an institution whose job that is. Ask who issued the other Rs 14,40,000 crore. Nobody did, so there is no answer. Four fifths of the money in the Republic of Sankhya was never issued by anyone. Issue is not the only way money comes into being.

The five to one gap is not a Sankhya oddity. Every country whose money is counted this way shows the same shape: a small issued quantity and a much larger total, with no printing press between them. Something other than issue is doing the work, and it does most of the work.

What does it mean to say lending creates deposits?

Here is the sentence, and it is worth reading twice because it sounds wrong the first time. When a loan is made, the borrower comes away holding a deposit. The new deposit is money by the same definitions that put every other deposit into the wider measure. Nobody handed it over, and it came from nowhere. The deposit began when the loan began.

Take a household in Sankhya that borrows Rs 8,00,000/- to build a room onto its shop. Before the loan, the household had no such money. After it, the household has Rs 8,00,000/- it can spend today. Now go looking for whoever is Rs 8,00,000/- poorer as a result. Everyone has that instinct, and the instinct has to go. There is nobody. No saver was asked. No account anywhere in Sankhya went down. Not one existing deposit had to move for the borrower's deposit to appear, and that is the entire surprise.

The reason it sounds wrong is that everybody's mental picture of lending is borrowed from lending between people. If a neighbour lends a household Rs 5,000/- then the neighbour has Rs 5,000/- less, and the total money between the two of them has not budged. The neighbour's picture is correct for the neighbour and exactly wrong for the banking system. A neighbour can only hand over money that already exists. The banking system, taken as a whole, does not have to.

Say what kind of statement this is. Over-reading it is easy. The claim is about the quantity of money in the Republic of Sankhya after the loan compared with before. The claim is not that any individual institution can lend without limit, not that lending is costless, and emphatically not a description of how anybody writes the transaction down. Each of those is a separate question with a separate answer, and none of them is needed to see that the quantity of money went up.

When the borrower spends the money, does it leave the system?

The obvious objection comes next. Fine, says the reader, a new deposit appeared. But the borrower did not take the loan in order to look at it. The household spends the Rs 8,00,000/- on a builder, and surely at that point the money is gone.

Follow it. The household pays the builder Rs 8,00,000/-. The household's deposit falls by Rs 8,00,000/-. The builder's deposit rises by Rs 8,00,000/-. Count the deposits in Sankhya before and after and the total is identical. A payment moved a deposit from one name to another and removed nothing. Money does not leave the system by being spent, it only changes whose name is on it. The process therefore runs in rounds instead of stopping at the first loan.

Sit with that for a second. The point is the least intuitive part of the mechanism and also the simplest. Spending feels like disappearance because it feels like disappearance to the spender. From above the whole economy, every rupee spent is a rupee received, and the received rupee is sitting in somebody's deposit that same evening. The builder now has money to pay a cement supplier, who then has money to pay a lorry driver, and at no point in that chain does the quantity of deposits fall.

What actually limits the process, then?

If a loan creates a deposit and spending it does not destroy the deposit, an obvious worry arrives: what stops this? The honest answer is that only what leaks out of it stops it. A round that leaked nothing would carry its whole amount forward for ever and the total would have no limit at all. So the limit is not some ceiling imposed from above. The limit is arithmetic: it is entirely set by the fraction of each round that drops out and never comes back round.

Two things drop out, and only two. The first is currency. People do not keep every rupee in a deposit. A vegetable seller ends the day with notes in a tin. A household keeps cash at home for a wedding. Whatever is held that way sits outside the deposit chain and cannot be lent onward by anybody. In Sankhya the cash held that way comes to 20.00 per cent of deposits, or Rs 3,00,000 crore against deposits of Rs 15,00,000 crore.

The second is reserves. A banking system has to hold a portion of what it takes in as reserves at the central bank rather than putting it back out. In Sankhya that portion is 4.00 per cent of deposits, or Rs 60,000 crore. Notice how much smaller it is than the first: Rs 60,000 crore against Rs 3,00,000 crore, one fifth of the size.

The two together give the total leak: 0.04 plus 0.20 is 0.24 of deposits. The 0.24 is what stands between the Republic of Sankhya and an unbounded quantity of money.

Now run it. Suppose a fresh deposit of Rs 3,60,000 crore appears in Sankhya. Of that, 20.00 per cent walks off as currency and 4.00 per cent is held as reserves, so Rs 86,400 crore leaks and Rs 2,73,600 crore is available to go round again as somebody's next deposit. Apply the same fractions to that, and to what survives it, and so on. Each round is 0.76 of the one before, and that is the definition of a geometric seriesA sequence in which every term is the same fixed multiple of the one before it. When that multiple is less than one the terms shrink and the whole infinite sequence adds up to a finite number.. A geometric series that shrinks has a finite total no matter how many rounds it is allowed to run.

Read the bottom row. Three things land at once. The rounds add up to deposits of Rs 15,00,000 crore, exactly the Sankhya deposit total. The currency column adds up to Rs 3,00,000 crore, exactly the currency Sankhya's public holds. The reserve column adds up to Rs 60,000 crore, exactly the reserves held at its central bank. The ladder is not a separate example; it lands on the published Sankhya figures because it is the same system taken one round at a time. Each row is rounded to the nearest crore and the row for rounds six onward is what remains after the first five, so the columns foot exactly.

One more thing hides in that table. Currency of Rs 3,00,000 crore plus reserves of Rs 60,000 crore comes to Rs 3,60,000 crore, and Rs 3,60,000 crore is where the ladder started. The whole of the opening amount ends up as the leakage from all the rounds put together. Put another way, the narrow measure is exactly the part of the money supply that had to be issued.

Why does the textbook multiplier overstate what actually happens?

Almost everyone meets this subject through one formula: one divided by the reserve ratio. Sankhya's reserve ratio is 4.00 per cent, and the formula gives 25.00. The number is clean, easy to remember, and wrong by a wide margin.

The actual ratio in Sankhya is already known and it needs no formula at all. The widest measure is Rs 18,00,000 crore and the narrow measure is Rs 3,60,000 crore, so the multiplier is 5.00. Set the two side by side: the formula says 25.00, the country says 5.00. One over the reserve ratio overstates the Sankhya multiplier exactly five times, and it does so for one reason: it counts one of the two leakages and ignores the other completely.

Unpacked, one over the reserve ratio carries a hidden assumption. The formula assumes that every rupee lent comes straight back as a deposit apart from the reserve portion. In plainer words, it assumes nobody keeps any cash. In a country where people hold no currency at all that assumption is true and the formula is right. In the Republic of Sankhya, where the public holds Rs 3,00,000 crore in notes, it is not remotely true, and the size of the error is the size of that habit.

Which of the two leakages does most of the limiting?

There is a formula that takes both leakages. Write the currency drain as a fraction of deposits and the reserve ratio as a fraction of deposits, then the multiplier is one plus the currency drain, all divided by the sum of the two. In Sankhya that is 1.20 divided by 0.24, or 5.00.

The argument can quietly mislead at exactly this point. The formula's 5.00 matches the 5.00 obtained by dividing Rs 18,00,000 crore by Rs 3,60,000 crore, and the match is tempting to present as a confirmation. A confirmation is not what it is. Currency is the currency drain times deposits and reserves are the reserve ratio times deposits, so multiplying the top and bottom of that formula by deposits turns it into currency plus deposits, over reserves plus currency. Currency plus deposits is the widest measure, and reserves plus currency is the narrow measure. The formula is the ratio of the two measures written a different way, so it can never disagree with the ratio and it confirms nothing whatsoever.

Which raises the fair question of why it is worth writing down at all, and the answer is that a rearrangement is not useless, it just does a different job. The rearrangement cannot check the total. Splitting the total is what it does instead, and the split is the finding. The bottom of the formula is 0.24, and that 0.24 is made of the currency drain at 0.20 and the reserve requirement at 0.04. The currency drain is five sixths of what limits the Sankhya multiplier and the reserve requirement is one sixth. The textbook formula puts the emphasis exactly the other way round.

Say plainly what that means. In the Republic of Sankhya, the habit of ordinary people carrying notes does five times as much to hold down the quantity of money as the rule the banking system has to obey. The rule is the part with an authority behind it, a name, and a number people quote. The habit has none of those things and it does most of the work.

What does a working reader actually do with this?

The household version is the one that lands. A family that keeps Rs 40,000/- at home for a wedding rather than in a deposit has performed a currency drain. Nothing in that is wrong or unusual, and it is not a large sum. But when a whole country does the same thing at once, the sum of all those tins and cupboards is Rs 3,00,000 crore in Sankhya, and it is doing five sixths of the work of holding down the money supply. A habit with no rule behind it is the binding constraint.

An analyst uses it in a specific and unglamorous way: to stop misreading a rise in deposits. When the deposit total in a country goes up, the instinct is to ask where the money came in from, as though it must have arrived from outside. Usually it did not arrive from anywhere. The deposits were lent into being, and asking which foreign flow or which government payment brought them in searches for something that was never there. The right question is what happened to lending, and the second right question is what happened to the two leakages.

A lender uses it to keep two questions apart that get muddled constantly. Whether an individual borrower can be lent to is a question about that borrower's creditworthinessWhether a particular borrower is likely to repay, judged from income, security and record. Creditworthiness is assessed borrower by borrower and is a separate subject from the system-level mechanism., and it has nothing to do with the mechanism above. Whether the system as a whole can create more deposits is a question about the two leakages and about the quantity of reserves available, and it has nothing to do with any individual borrower. Confusing a judgement about one borrower with a statement about the whole system is the commonest way this subject goes wrong in argument.

And somebody watching system liquidityWhether the whole banking system is short of funds at the central bank on a given day, or holding more than it needs. System liquidity is a reading for the system rather than for any one place, and it is covered where liquidity conditions are covered. uses it to know what a change in reserves can and cannot do. Reserves are one of the two leakages, and in Sankhya they are the smaller one. Adding to them loosens the smaller of two constraints, a real effect and a modest one. Expecting the money supply to move by one over the reserve ratio is the error that forgetting the larger constraint produces.

What does this account deliberately leave out?

Three things, and naming them is part of the account rather than an apology for it.

The account says nothing about whether any particular loan should be made. Everything above is a statement about what happens to the quantity of money when lending goes on, and it is equally true of lending that turns out well and lending that turns out badly. An account of how deposits come into being says nothing at all about whether a given one should have.

The account says nothing about who is worth lending to. Worth is a judgement about one borrower at a time, made on evidence about that borrower, and the mechanism above runs identically whoever the borrower is.

And it says nothing about how any institution records what it has done. Recording is a whole subject in its own right, it lives with accounting and financial statements, and the striking thing is that the mechanism above is complete without a single line of it. The quantity of money in the Republic of Sankhya went from one number to another, the two leakages explain how far it could go, and the arithmetic closed to the rupee, all without opening anybody's records. The account belongs at that level.

The Republic of Sankhya is invented.
Educational material. Not advice on any investment, tax, budget or market position.