The Money Multiplier

The Bank of England yesterday published a report assessing the effect of Quantitative Easing on the UK Economy.

While looking into this, I started to wonder about the size of the Money Multiplier effect in the UK.

The Money Multiplier is an effect where if you print some extra money, it has a disproportionate effect on the total amount of money deposited in banks.

It’s pretty simple: Let’s say we print £100 and give it to someone. They put it in their bank account. Banks will keep some (so that people can withdraw money) and lend out the rest. Let’s say they keep 10% and lend out the rest. So they lend £90. The borrower spends it or puts it in the bank; either way it eventually ends up in a bank account. So now the bank has deposits worth £190. Of the new £90, they keep 10% (£9) and lend out the rest (£81). Which ends up back in banks – so now the deposits are worth £271. And so on.

The Money Multiplier tells you what you have to multiply the new money by to find out the total amount of all the new bank deposits that will result (based on the percentage which gets held back each time.

For example, with a Reserve of 2%, the Money Multiplier works out at 50.

In some countries, banks are required to keep a minimum amount, known as the ‘Reserve Requirement’. In the UK there is no requirement, but they keep some voluntarily.

The interesting thing that happened around the time covered by the Quantitative Easing report, was that the Reserve Amount in the UK seems to have increased spectacularly.

When Quantitative Easing started in March 2009, the total amount deposited by UK banks with the Bank of England amounted to £41.6bn and the total amount deposited in UK bank accounts was around £3.2tn. Doing the calculation in reverse, this implies a Reserve Amount of 1.3%, which is pretty small in historical terms, and compared with other countries.

The Government then commenced a period of 11 months of Quantitative Easing, in which they created £200bn of new money. By the end of that period, in January 2010, the reserves had gone up to £154bn, whilst the total amount deposited at banks had barely increased at all, going up to just £3.3tn. Plugging these numbers into the Livesheet above tells us the reserve amount had increased to 4.7%.

At the time, we heard that banks had been refusing to lend despite the Quantitative Easing. It’s clear that they felt less confident in their assets and in the wake of the Northern Rock debacle, felt more vulnerable to the possibility of a run on a bank; and increasing their reserves gave them a safety net.

And in that context, it’s easy to see why the Quantitative Easing was necessary: if banks had tried to increase their reserve amounts without the Quantitative Easing, it would have had to be associated with an enormous reduction in the amount deposited in bank accounts (from £3.2tn to £891bn)

which would have taken a very long time and been uncomfortable for everyone involved.

It is interesting to wonder what will happen next. If confidence grows and banks end up reducing their reserves to, say, 2%, over a relatively short period of time, then if the available reserves stay at their current level of £154bn this will increase the total bank deposits to £7.7tn – resulting in massive inflation and asset bubbles. Presumably as that starts to happen, the Bank of England will have to take measures to reduce the money supply. The normal mechanism for controlling an excess money supply would be to increase interest rates to reduce the rate at which new money is created. Perhaps in this case it won’t be enough and they’ll be required to undo some of the Quantitative Easing of the last few years. Time will tell.

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