To increase transparency in science, some scholarly journals are publishing peer review reports. But it is unclear how this practice affects the peer review process. Here, we examine the effect of publishing peer review reports on referee behavior in five scholarly journals involved in a pilot study at Elsevier. By considering 9,220 submissions and 18,525 reviews from 2010 to 2017, we measured changes both before and during the pilot and found that publishing reports did not significantly compromise referees’ willingness to review, recommendations, or turn-around times. Younger and non-academic scholars were more willing to accept to review and provided more positive and objective recommendations. Male referees tended to write more constructive reports during the pilot. Only 8.1% of referees agreed to reveal their identity in the published report. These findings suggest that open peer review does not compromise the process, at least when referees are able to protect their anonymity.