The most important paragraph in the IMF World Economic Outlook

68 words of wonkishness.

The IMF's World Economic Outlook (pdf) – a 230-page tome detailing predictions on nearly every aspect of the world's economy collated by the international organisation – always gets attention for the calls it makes.

The October edition downgrades expected global growth for 2013 from 3.9 per cent to 3.6 per cent, and also cuts predictions for China (down to 8.2 per cent for 2013), the US (expected to grow by 2.1 per cent in 2013, down from 2.3 per cent in July's prediction) and the UK (now expected to grow by just 1.1 per cent next year, and to contract by 0.2 per cent this year).

But the predictions are not the most important passages in this edition of the Outlook. Those are found in a short box-out titled Are We Underestimating Short-Term Fiscal Multipliers?

The fisc§al multiplier is the effect government spending has on GDP. Money spent by the government doesn't disappear – it is respent, again and again. If a teacher gets a pay rise, their consumption is likely to rise in line with it; if all teachers get pay rises, that increase in consumption may be enough to affect the aggregate demand in the economy. In an economy which isn't being stretched to its limits – that is, one without full employment, or serious capital equipment shortages – that increase in aggregate demand will result in an increase in GDP.

The existence of the fiscal multiplier is a matter of fact, but the magnitude of it is contested. And that's where the IMF enters the scene, on page 42:

The main finding, based on data for 28 economies, is that the multipliers used in generating growth forecasts have been systematically too low since the start of the Great Recession, by 0.4 to 1.2, depending on the forecast source and the specifics of the estimation approach. Informal evidence suggests that the multipliers implicitly used to generate these forecasts are about 0.5. So actual multipliers may be higher, in the range of 0.9 to 1.7.

Emphasis mine. When deciding how much to spend, governments have been assuming that every pound they spend increases GDP by 50p – but it may increase it by as much as £1.70.

The reason this is so very important is that fiscal multiplier is usually appealed to not when deciding how much to spend, but how much to not spend. When governments are planning austerity packages, they have to be wary of the fact that large cuts to government spending will inevitably cause a decrease in output, and so they either have to be prepared to take that hit, or come up with a reason why slashing spending will cause an increase in output through some other mechanism.

That is easy enough to do if you are trying to account for a fiscal multiplier of 0.5: you can make the arguments, which Osborne and Cameron rehearsed repeatedly, that the public sector is crowding out the private; that the government spending which is being cut is particularly inefficient; or that the confidence fairies will reward your thriftiness with growth.

When there is the chance that the fiscal multiplier is three times that, austerity becomes much more likely to involve damaging drops in output.

There was once a time when the government pegged its credibility to that of the IMF – back when George Osborne was proud about Britain's credit ratings, and the international community was behind his plans. Those days are gone, and have been since Christine Lagarde made her own attack on austerity. But the economists at the treasury may be more inclined to listen to the wonkish findings of the World Outlook than the political interventions of the fund's leader. We can only hope they are prompted to re-do the sums.

The IMF headquarters. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Ansbach puts Europe's bravest politician under pressure

Angela Merkel must respond to a series of tragedies and criticisms of her refugee policy. 

Angela Merkel, the Chancellor of Germany, is supposed to be on holiday. Two separate attacks have put an end to that. The first, a mass shooting in Munich, was at first widely believed to be a terrorist attack, but later turned out to be the actions of a loner obsessed with US high school shootings. The second, where a man blew himself up in the town of Ansbach, caused less physical damage - three were seriously injured, but none killed. Nevertheless, this event may prove to affect even more people's lives. Because that man had come to Germany claiming to be a Syrian refugee. 

The attack came hours after a Syrian refugee murdered a pregnant Polish woman, a co-woker in a snack bar, in Reutlingen. All eyes will now be on Merkel who, more than any other European politician, is held responsible for Syrian refugees in Europe.

In 2015, when other European states were erecting barriers to keep out the million migrants and refugees marching north, Merkel kept Germany's borders open. The country has resettled 41,899 Syrians since 2013, according to the UNHCR, of which 20,067 came on humanitarian grounds and 21,832 through private sponsorship. That is twice as much as the UK has pledged to resettle by 2020. The actual number of Syrians in Germany is far higher - 90 per cent of the 102,400 Syrians applying for EU asylum in the first quarter of 2016 were registered there. 

Merkel is the bravest of Europe's politicians. Contrary to some assertions on the right, she did not invent the refugee crisis. Five years of brutal war in Syria did that. Merkel was simply the first of the continent's most prominent leaders to stop ignoring it. If Germany had not absorbed so many refugees, they would still be in central Europe and the Balkans, and we would be seeing even more pictures of starved children in informal camps than we do today. 

Equally, the problems facing Merkel now are not hers alone. These are the problems facing all of Europe's major states, whether or not they recognise them. 

Take the failed Syrian asylum seeker of Ansbach (his application was rejected but he could not be deported back to a warzone). In Germany, his application could at least be considered, and rejected. Europe as a whole has not invested in the processing centres required to determine who is a Syrian civilian, who might be a Syrian combatant and who is simply taking advantage of the black market in Syrian passports to masquerade as a refugee. 

Secondly, there is the subject of trauma. The Munich shooter appears to have had no links to Islamic State or Syria, but his act underlines the fact you do not need a grand political narrative to inflict hurt on others. Syrians who have experienced unspeakable violence either in their homeland or en route to Europe are left psychologically damaged. That is not to suggest they will turn to violence. But it is still safer to offer such people therapy than leave them to drift around Europe, unmonitored and unsupported, as other countries seem willing to do. 

Third, there is the question of lawlessness. Syrians have been blamed for everything from the Cologne attacks in January to creeping Islamist radicalisation. But apart from the fact that these reports can turn out to be overblown (two of the 58 men arrested over Cologne were Syrians), it is unclear what the alternative would be. Policies that force Syrians underground have already greatly empowered Europe's network of human traffickers and thugs.

So far, Merkel seems to be standing her ground. Her home affairs spokesman, Stephan Mayer, told the BBC that Germany had room to improve on its asylum policy, but stressed each attack was different. 

He said: "Horrible things take place in Syria. And it is the biggest humanitarian catastrophe, so it is completely wrong to blame Angela Merkel, or her refugee policies, for these incidents." Many will do, all the same.