HAMBURG—In 1982, a young Turkish immigrant named Kemal Sahin opened a new 430-square-foot gift shop on a busy commercial street in Aachen, Germany. Sahin didn’t want to start his own business, but he had to. It was his only chance to stay in the country. From a farm family in an isolated Anatolian mountain town in Turkey, Sahin arrived in Aachen as a teenager carrying nothing but an old suitcase, two packs of cigarettes, and some money pinned inside his jacket. He worked his way through university to earn an engineering degree on full scholarship. He’d thought this would lead to a good, entry-level job in German industry. “Instead,” he recalls, “they told me I had to leave.”

Since he was a foreigner, Sahin couldn’t obtain a work permit in his field regardless of education, skill, or talent. There was only...

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