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"Here is the biggest problem we face," the senior official from Chancellor Angela Merkel's government told me as he pulled out a pen and drew a pie-graph circle on his napkin.

"This is the working-age population of Germany – 45 million people." Then he drew a thick slice, almost a sixth of the circle: "This is 6.7 million people, the number of working-age people we expect to lose over the next 10 years." That's the very large number of people who will reach retirement age or move away, minus the much smaller number who will reach working age or migrate to Germany.

Losing almost seven million income-earning, tax-contributing workers is expensive, especially since most will become pension-earning, increasingly public-health-care-requiring people, in a country where those services are generous.

The gap between the tax-contributing and government-dependent population is known as the dependency ratio. Germany is one of many Western countries that are about to see it more than double. In 2000, it had four working-age people for every senior; by 2035, it will be nearly seven seniors for every 10 working-age people. When you subtract that many taxpayers, the numbers just don't add up, and government is crippled.

The German official's words were similar to those I've heard recently in France, Sweden, Italy and in many Canadian provinces. Dependency ratios have received little attention over the past six or seven years because the economic crisis obscured the problem: Economies needed fewer workers. And in Europe, the devastated countries of the south sent millions of migrants north, easing the work force pressure. Now there's a search for solutions.

"Here," the official said, sketching two much smaller pie slices within the larger one, "are the two things we hope to do to make it smaller."

The first approach, most dramatically taken in Sweden, is to expand the workforce by making it easy for women to enter the job market. The Swedes have among the highest female employment rates in the Western world; this was achieved by making childcare universal and free and demanding flexible policies around work hours that made it easier for mothers (and fathers) to move in and out of work. The French introduced similar policies a decade ago and have seen their female labour-force participation rate rise sharply. Germans lag behind; the country still maintains half-day schooling in many regions and a formidable prejudice against mothers working.

The Germans calculate that these female work force programs – helped by Ms. Merkel's success in winning over her Christian Democratic party's more conservative factions – could theoretically keep two million of those missing 6.7 million people in the work force, if they became near-universal.

A second approach is to try to get more people off of the margins of the work force and into full working life. This involves changing welfare and social-security benefits so that people can both collect them and work. It involves redesigning school systems so they discourage young people from dropping out and promote near-universal postsecondary education. It involves encouraging companies to hire pensioned retirees, on contracts, into skilled positions. It involves the creation of apprenticeship systems to get those who have left school to learn skills.

Germany is focusing on the last two, with prominent retiree-hiring and apprenticeship programs, and it hopes that these programs will reduce the missing-worker slice by one million. France is focusing on changing its school system. Britain has used flexible welfare benefits, with some success. Japan, the first country to feel the effects of a sharpening dependency ratio in a bad way, has tried many of these things.

A third approach is to try to get people to have more children. A decade ago, France offered couples big monthly payments if they had a third child. This raised the fertility rate from 1.8 children per family to almost 2.1 – the number at which populations stop shrinking and become stable. It helped the missing-worker problem somewhat, but not fully.

It is the rest of that slice – the remaining 3.7 million missing workers in Germany – that poses a larger political problem. It won't be addressed with internal changes.

As Germans and others are learning, the only remaining solution is immigration – at a moment when it's not exactly politically popular. That's why right-wing parties, such as Ms. Merkel's Christian Democrats and British Prime Minister David Cameron's Conservatives, are abandoning their old anti-immigrant stances and selling the public on immigrant settlement programs. It's why European officials have been besieging Canada to find out how our system works. They don't want to be in power when their country runs out of taxpayers.