Multinational companies shift about 40% of the profits they earn outside their home countries into tax havens, eluding tax-collection efforts, according to an analysis that points to persistent gaps in government revenue collection.

U.S. companies are among the most aggressive users of profit-shifting techniques, which often relocate paper profits without bringing jobs and wages, according to the study by economists Thomas Torslov and Ludvig Wier of the University of Copenhagen and Gabriel Zucman of the University of California,...