Trump might be keeping tourists away from the U.S.

Is the “Trump effect” scaring off international tourists from the U.S.?

That’s a key question for the U.S. tourism industry heading into the important summer season.

After several indications of weakening demand to visit the U.S., some recent data looks more reassuring. The U.S. Travel Association said Tuesday that its Travel Trends Index indicated that international travel to the U.S. rose about 4 percent in April compared to a year ago. The increase was a pleasant surprise even to the association’s chief executive, according to the Associated Press.

The dollar’s recent weakness likely has helped coax visitors stateside. (All else being equal, a weaker dollar makes it cheaper for Europeans and other international travelers to visit America.)

But some in the industry remain concerned that anti-foreigner rhetoric and policy proposals by President Donald Trump, including a push to get the Supreme Court to reinstate his travel ban for six Muslim-majority countries, could sour some potential tourists on the U.S.

Jeff Glueck, CEO of check-in app Foursquare, said in a blog post that his company’s recent analysis of user geolocation data suggested a marked drop-off in foreign tourism to the U.S. beginning in October, the eve of our presidential election, which was tinged with nationalist themes. (Although, for the record the U.S. dollar was also strengthening in late 2016, which is another possible reason why travel weakened over that period.)

Glueck said that slide has shown “no sign of recovery” since, including a 16 percent decline in U.S. tourism in March compared to the year-ago period. Even business travel, which was recently up 3 percent in the U.S. compared to a year ago, has been soft relative to the rest of the world, which has shown a 10 percent increase, according to the Los Angeles Times.

Other observers have also noted softness in the foreign travel to the U.S. In a conference call with analysts following his company’s quarterly earnings report in early May, MasterCard CEO Ajay Banga was asked about potential problems. He noted that there was anecdotal evidence of “some slowdown” in recent incoming travel to the U.S.

But Banga advised a wait-and-see approach overall, adding: “Part of it could be concerns around the political and stability of the social environment. It’s tough to say. And I wouldn’t read too much into it yet. I think if it continues for another quarter, that will be a matter of some concern.”

That weak showing has clearly caught the attention of Trump’s Commerce Secretary Wilbur Ross. He recently struck a reassuring tone in remarks to a D.C. conference organized by the U.S. Travel Association.

“Let me be clear: America is open for business, America is open for travel and open to the millions of international visitors who wish us well,” Ross said.

On paper, the administration is somewhat less enthusiastic about promoting global tourism, including programs beside the well-publicized travel ban. Case in point: The White House’s recent budget proposal seeks to eliminate all funding for Brand USA, a federal program to promote international tourism.