When Pope Francis ascended to the chair of St. Peter in March 2013, the world looked on in wonder. Here at last was a pope in line with the times, a man who preferred spontaneous gestures to ritual forms. Francis paid his own hotel bill and eschewed the red shoes. Rather than move into the grand papal apartments, he settled in the cozy guesthouse for visitors to the Vatican. He also set a new nondogmatic tone with statements like “Who am I to judge?”

Observers predicted that the new pope’s warmth, humility and charisma would prompt a “Francis effect” — bringing disaffected Catholics back to a church that would no longer seem so forbidding and cold. Three years into his papacy, the predictions continue. Last winter, Austen Ivereigh, the author of an excellent biography of Pope Francis, wrote that the pope’s softer stance on communion for the divorced and remarried “could trigger a return to parishes on a large scale.” In its early days, Francis’ Jesuit order labored to bring Protestants back into the fold of the church. Could Francis do the same for Catholics tired of headlines about child abuse and culture wars?

In a certain sense, things have changed. Perceptions of the papacy, or at least of the pope, have improved. Francis is far more popular than his predecessor, Pope Benedict XVI. Sixty-three percent of American Catholics approve of him, while only 43 percent approved of Benedict at the height of his popularity, according to a 2015 New York Times and CBS News poll. Francis has also placed a great emphasis on reaching out to disaffected Catholics.

But are Catholics actually coming back? In the United States, at least, it hasn’t happened. New survey findings from Georgetown’s Center for Applied Research in the Apostolate suggest that there has been no Francis effect — at least, no positive one. In 2008, 23 percent of American Catholics attended Mass each week. Eight years later, weekly Mass attendance has held steady or marginally declined, at 22 percent.