As of 2019 there is no federal tax penalty for not having health insurance. However, those who live in MA, DC, NJ, CA, or RI may face a state tax penalty for not having coverage. Regardless of your state residence, it is important to have coverage in case you get sick or injured and have to return to the U.S. to receive care, so it would be worthwhile to explore what coverage options you may have while studying abroad.