Several colleagues and I recently published a working paper in which we explore the relationship between the overseas activities of U.S. services multinationals and employment in the United States, using some novel quantitative methods accompanied by case studies. We find that the effects of service firms' overseas activities on U.S. employment appear to be largely positive. But our methods are experimental, and we need feedback to make our work better. Your comments are heartily welcomed.
The table below (from page 14 of the paper) summarizes one of our main findings: that intrafirm exports of services by U.S. multinationals appear to be a significant supporter and creator of jobs in the US.