In fact, the attacks do fit a pattern: According to the Cologne police, 40 percent of the city’s immigrants from northern Africa become delinquent, mainly for theft, within their first year in Germany. Another problem, the police say, is that in order to avoid deportation, many asylum seekers from this region ditch their passports so that their home country is unknown.

The charge that economic immigrants are masquerading as refugees, long denied here — including by Ms. Merkel herself — is now painfully, undeniably true. And why wouldn’t it be? If you’re a 20-something Moroccan without any job prospects, and suddenly an airline ticket to Istanbul equals an entry ticket into Europe, wouldn’t you take your chance?

The problem, as Cologne demonstrates, is that potentially thousands of these men are criminals, with no other aim than to rob and betray their hosts. This is despicable and unbearable.

Ms. Merkel should acknowledge that she underestimated this problem. The continuation of Willkommenskultur depends on her embracing an Ehrlichkeitskultur. In particular, she must do three things.