DONALD TRUMP launched his presidential campaign with a promise to build a wall along the United States-Mexico border in order to stem the tide of undocumented immigration. In fact, those flows were already in steep decline long before he introduced the proposal. The number of apprehensions of people attempting to cross illegally peaked in 2000, when America′s Border Patrol made more than 1.6m arrests, over 98% of which were of Mexicans. Over the course of George W. Bush′s administration, this number dropped to around 1m annually. During Barack Obama′s presidency, the rate fell even more precipitously, averaging just 400,000 a year. Moreover, in 2016, only 47% of the apprehensions involved Mexicans.

Counting arrests does not necessarily yield a reliable estimate of the number of border-crossers who evade detection. The authorities′ rate of success at catching illegal immigrants can vary, and they may wind up detaining the same people multiple times. Nonetheless, the Pew Hispanic Centre estimates that the total who do make it through has fallen as well, to less than a third of its maximum level.

The causes of this decline are open to debate. In the early 2000s, Republican politicians from border states lobbied the federal government to build a fence. In response, Congress authorised the construction of 700 miles (1,125 km) of fencing in 2006, covering about a third of the total distance from the Pacific Ocean to the Gulf of Mexico. Now, nearly a decade after the fence was built, arrests have dwindled almost everywhere—both in areas separated from Mexico by existing fences and in those where the Rio Grande forms a natural obstacle. The only region that has seen an uptick in arrests is the Rio Grande Valley, which contains fencing on part but not all of its slice of the border. Whether the fence is responsible for this trend is contested: the end of America′s housing boom, which created large numbers of construction jobs filled by Mexican immigrants, probably also played an important role.

Mr Trump has no doubts about the efficacy of physical barriers. On January 25th he signed an executive order calling for the construction of a border wall, which could rise some 40 feet (12 metres) high and stretch across 1,000 miles. It seems less likely that he can fulfil his vow to make Mexico pay for the project. The country′s government has scoffed at this notion, and Enrique Peña Nieto, its president, announced the next day that he would cancel a planned visit to Washington.