Germany is struggling to cope with immigrants. The authorities have lost count because many have not registered. Millions are in transit. The discussion among Germans has understandably focused on the political consequences, especially on whether Angela Merkel has been wise to stick to her open-door policy. One way to answer this question is to look at the economic impact of the refugees.

I understand that one of the reasons, though not the main one, the German chancellor chose to invite refugees is to fix an imminent demographic squeeze. The immediate issue is not the total population size, which for now is relatively stable at a little over 80m. The more pressing issue is the decline in Germany’s working age population. This leads to an increase in the dependency ratio — the number of those in work who support those not in work.

The Federal Statistics Office estimates that the number of people in the 20-65 age group is set to fall from 49.2m in 2013 to 48.8m in 2020. This is on the assumption of weak immigration, defined as a fall of average net immigration from 500,000 in 2014 to a little over 100,000 by the end of the decade. In another scenario under which net immigration would fall to 200,000 the working population would stabilise at 49.2m. Since the sheer number of refugees puts us well beyond this second scenario, one might conclude that net immigration would fix the problem for as long as it persists and is large enough.