TRUMP Tower, in midtown Manhattan, has become a modern-day Mount Vernon. Tourists have long visited George Washington’s homestead. Now they venture through Trump Tower’s brass doors to ogle the decor—“it’s so gold,” said a German teenager standing near the lobby’s waterfall on a recent afternoon—or buy souvenirs. The Choi family, visiting from South Korea, wandered the marble expanse with their new “Make America Great” hats (three for $50). The question for America’s hoteliers and airlines is whether such visitors are just anomalies. A strong dollar is one reason for foreigners to avoid visiting America. Donald Trump may prove another, suggests a growing collection of data. Yet measuring the precise impact of Mr Trump’s presidency on travel is difficult. In addition to the currency effect, many trips currently being taken to America were booked before his election. Marriott, a big hotel company, reported an overall increase, compared with a year earlier, in foreign bookings in America in February.

But Arne Sorenson, Marriott’s boss, has voiced concern about a potential slump in tourism. In February, ForwardKeys, a travel-data firm, reported that in the week after Mr Trump first tried to ban travel from seven Muslim-majority countries, international bookings dropped by 6.5% against the same period in 2016. Hopper, a travel app, found that average daily searches for flights to America have declined in 99 countries since Mr Trump tried to issue his travel ban, compared with the last weeks of Barack Obama’s term. Russia is one of the few places where demand has risen (see chart). Tourism Economics, a forecaster, expects 2m fewer foreign visits to America this year, a 1% drop from 2016. Without Mr Trump it had expected a 3% jump.

Some sort of fall-off would be unsurprising. On March 6th Mr Trump issued a new, revised travel ban from six Muslim-majority countries. The measure is mired in litigation, but that does not give visitors from the affected countries much comfort. On March 17th Rex Tillerson, the secretary of state, gave broad instructions for consular officials to identify “populations warranting increased scrutiny” and adjust visa-processing accordingly. Such vetting would cover a much broader swathe of the globe than the ban. Then officials barred on-board laptops for travellers from some airports in the Middle East and north Africa. (Britain issued a similar prohibition.)

The laptop ban has simply prompted some business travellers who work in the Middle East to book flights with a layover in Europe so that they can use laptops onboard, says Greeley Koch of the Association of Corporate Travel Executives. But closer scrutiny of visa applications will probably lead to delays and fewer visas. Tourists who oppose Mr Trump’s policies may go elsewhere. This week Emirates, an airline based in Dubai, said it would reduce flights to five American cities from May, owing to lower demand.

The industry has been here before. International tourism in America slumped by around 3% each year from 2000 to 2006. Most analysts blame not only the attacks of 2001 but stricter visa rules and anti-American sentiment abroad. Countries that had the dimmest view of America, according to surveys during that period, tended to see drops in travellers there, says Adam Sacks of Tourism Economics. “We are facing a potential rerun,” he says. Dara Khosrowshahi, head of Expedia, an online booking site, has noted that American hotels and airlines are already cutting prices in an attempt to lure travellers.

America’s main tourism lobby group is now urging Mr Trump, who presumably has some sympathy with other hoteliers, to emphasise that the country continues to welcome foreign visitors despite all the new security measures. The tourism agency for New York city, NYC & Company, is trying to counteract negative rhetoric from Washington, DC with advertisements in Britain, Germany, Mexico and Spain.

In the capital itself, any loss of visitors from abroad may be offset by a surge in angry American ones. After dates were finalised for a women’s march to protest Mr Trump’s inauguration, hotel bookings spiked. Elliott Ferguson, head of the city’s tourism group, expects a similar surge for this year’s Pride Parade, on June 10th.