The European debate about quantitative easing has reminded me of Zeno’s paradox of motion: Achilles could never catch up with a tortoise — because whenever he had bridged the distance between them, the tortoise advanced. Same here: whenever the conditions seemed to be in place for QE, new ones popped up.

All that has changed. The European Central Bank voted to elevate the 1 trillion euro increase in the size of its balance sheet from something it expected to happen to something it intends to accomplish. This is more than a rhetorical change. Without QE the target cannot be reached. By committing to this number, the ECB in effect agreed to QE.

Those who have opposed the programme know that once the ECB has a balance sheet target, QE will follow by default. The ECB’s existing programmes are not big enough to reach that goal.

In light of this new situation, the question is no longer whether QE will happen but how it will work. I would expect the size of any programme to be about 500 billion euros. With that, the balance sheet target could be in reach. So what would 500 billion euros buy?

The total amount of the Eurozone’s government debt is about 9 trillion euro, so such a programme would just be 5.5 per cent of the total. Compare this to the UK, where the Bank of England’s stock of government debt was about 25 per cent of the total issued as of 2013.

If the ECB wanted to do as much as the BoE did from 2009 onwards, in relative terms, it would have to commit to asset purchases of more than 2 trillion euro. In fact, it has to do quite a bit more because it has started much later, and because the situation in the Eurozone is more serious.

Those on the ECB’s governing council who oppose QE fear that it would trigger a larger programme later on. This is why I expect Berlin to mount a legal challenge in the European Court of Justice. A 2 trillion euro programme, or something approaching that, would have a similar economic effect to a Eurozone bond — that is, a jointly issued debt security — which is something Germany has been resisting.

In that scenario the ECB would absorb a big chunk of the outstanding debt of highly indebted Eurozone countries, and keep it on its books forever. The alternative to a large programme is an inadequate one — for example, one that stops at 500 billion euro. It would meet less opposition in Berlin. Unfortunately, it would also be economically irrelevant.

To see this, one should consider the channels through which QE works. The most direct impact would be on the interest rates of the securities purchased. If the central bank buys five-year government bonds, the price of those bonds will rise and the yield will fall. Since those bonds serve as a benchmark for bank loans, the interest rates on banknotes may fall as well, in theory, though probably not in the Eurozone.

Then there is the “portfolio rebalancing channel”: when banks sell bonds to the ECB, they will need to buy something else instead. They might lend it out. They might buy other risky securities. This may well be the most important effect but it will probably not be as effective as it was in the US and the UK, when asset prices were lower.

What about the exchange rate? This is the most overrated channel. The euro’s trade-weighted exchange rate has fallen by only 4 per cent in the past year. It could come down a little further, but this is not going to do the heavy lifting. The Eurozone is simply too big for that.

The only truly significant conduit of a QE programme would be a debt relief channel. If the ECB were to buy, and retire, a quarter of Italian debt, life in Italy would become a lot easier. That, however, is not going to happen — either because the programme is too small or, if not, Berlin would challenge it legally.

If you want to push the money through these channels into the economy, you will need a lot of money and a lot of pushing. Ideally, you would not start from here but from where the US Federal Reserve or the Bank of England started in 2008 and 2009 respectively. My fear is that a European QE programme will happen but still stay trapped in Zeno’s paradox.

— Financial Times