Harvard professor Gita Gopinath’s appointment as chief economist of the International Monetary Fund raises a question about her native India: Is IMF Managing Director Christine Lagarde more likely than Prime Minister Narendra Modi to hire someone with Ms. Gopinath’s stellar academic credentials?

In the past two years, three high-profile Western-trained economists have exited important policy-making positions in India to return to academia in the U.S. A rising drumbeat of nativist sentiment, increased political interference...