EIGHT “carpet shoes” outside Jim Chilton’s house testify to the frugal innovation of Mexico’s people-smuggling industry. These shoes, bound pieces of denim with soft soles designed to leave no trace in the Arizona desert, have been lost or abandoned by illegal immigrants traversing Mr Chilton’s 50,000-acre cattle ranch, which stretches to the Mexican border. Mr Chilton displays them to help convince visitors that, whatever the politicians in Washington may say, America’s southern border is far from secure.

Whether the country gets a long-overdue reform of its immigration system, including a route to citizenship for the 11m illegal migrants now living there, may hinge on this question. The bill currently being debated in the Senate devotes $4.5 billion to border security, including yet more drones, fences and guards with guns. But many Republicans, recalling the multitudes that arrived after Ronald Reagan’s amnesty in 1986, want even more.

Senator Marco Rubio, a Republican point man on immigration, has said the bill needs tougher border measures to win his support. Legislation may also struggle to get through the Republican-controlled House of Representatives. On June 18th John Boehner, the Speaker, suggested he would not allow a vote without the support of a majority of Republicans.

John Cornyn, a Texas Republican senator, says no illegal alien should be granted a green card (ie, permanent residency) until the southern border is 90% secure. It is not clear that this target makes sense. Driving back late from the border (marked by a waist-high scrappy barbed-wire fence) through Mr Chilton’s ranch, the difficulties of measuring security become clear. A passing agent explains that a ground sensor has detected movement; he is on his way to investigate. Asked how he will spot anyone in the dark, he agrees that it is hard; he will use a torch and try his best. An agent encountered a little later hopefully mentions a helicopter, but none appears.

The Border Patrol, which is charged with nabbing illegal crossers between official entry points, defines its effectiveness by the number of people it catches (or those that turn back) as a proportion of those it detects. By this formula the Border Patrol in Tucson sector, which includes Mr Chilton’s ranch as well as the area around an official crossing at Nogales, is 87% effective. But estimates for the true overall figure range widely; some put it as low as 30%. For such a hot topic, the available data are, as a report from the Council on Foreign Relations puts it, “distressingly sparse”.

The numbers are clearer on the input side. When Congress last tackled immigration reform, in 2007, there were 15,000 Border Patrol agents; today there are 21,000. Ten Predator drones patrol the skies, tower-mounted cameras dot the deserts and ground sensors monitor land movements. Mitch Merriam, deputy commander of the Arizona Joint Field Command, says he had enough agents until sequestration cuts forced the patrol to get “pretty darn creative”. According to the Migration Policy Institute, a think-tank, border enforcement costs $18 billion a year, more than all other federal criminal-law-enforcement agencies combined.

To bolster its argument that the border is secure, Barack Obama’s administration points to the drop in apprehensions at or near it (see map). These bottomed out in 2011, and as the once-porous Tucson sector has tightened there are signs that the action may be moving east, to Texas. Apprehension numbers are a poor proxy for border security, but few dispute that, compared with the free-for-all of the late 1990s and early 2000s, today’s border is calm (see charts).

Why might this be? Economics probably matters more than enforcement. America’s downturn cost many illegal migrants their jobs, just as opportunities were blossoming back home in Mexico. In the past two years Mexico’s economy has grown at a healthy 3.9% annually, creating jobs (albeit at much lower pay than in America). In the longer term, demography is also likely to slow the flow of migrants. The number of 15-24-year-olds in Mexico and El Salvador will start declining between 2015 and 2020. Since illegal crossers tend to be young men, this will surely ease the pressure on the border. And over the next 40 years fertility rates in both countries are forecast to drop below America’s. Walls and drones do make a difference. Gordon Hanson, an economist at the University of California, San Diego, credits tighter security for one-third of the drop in migration between the late 1990s and 2010. Spending yet more money could reduce crossings further, he says—although he believes that America is already inflicting economic self-harm by spending so much to keep workers out.

Migrants pay taxes, too

A new report from the Congressional Budget Office (CBO), released on June 18th, makes a broader point. It forecasts that the Senate immigration bill would reduce the federal budget deficit by $197 billion over the next decade and $700 billion over the decade after that. By bringing illegal workers into the mainstream and allowing more visas for newcomers, both skilled and unskilled, it would raise American output and productivity. The CBO predicts that the economy would be 5.4% bigger in 2033 because of the bill, and that average wages would be slightly higher.

John McCain, Arizona’s senior senator and a co-author of the Senate bill, says that better technology could let the Border Patrol know almost exactly where and when people are crossing. He also wants to increase guest-worker slots and force employers to check whether their workers are legal. Some 40% of America’s undocumented immigrants have overstayed visas rather than crossed illegally, he adds.

Tighter security pushes border-crossers to more remote areas. Out in the desert, dozens of miles from Nogales’s steel-and-concrete fence, the chances of detection are slimmer. But so are the odds of survival; the number of bodies recovered by border agents has remained stable even as apprehensions have plummeted (see chart). As Robin Reineke of the Missing Migrant Project points out, these are merely the bodies that agents chance upon; the true toll must be higher.

Nor is a lonely death from exposure the only risk. Once, migrants would slip $300 to a coyote in a border town who would guide them across. Today illegal crossings are controlled by criminal gangs, which charge more and care less. People- and drug-smuggling routes have merged, and many migrants carry bales of dope to fund their journey. Their guides may assault or abandon them, or they may be robbed of their cargo by “rip crews” (US-based bandits). Mr Chilton and his wife, Sue, encounter fewer crossers these days, but those they do see sometimes carry AK-47s.

Fortifying the border has two immediate effects: it makes it easier to catch illegal migrants and it deters others from trying. Raising the cost of crossing must keep out some economic migrants. But the record number of deportations under Mr Obama has created a giant class of expelled foreigners with deep roots in the United States. One survey of recent deportees found that 22% had offspring who were American citizens. Parents separated from their children are unlikely to be put off by extra helicopters or double fencing. The policy, says Ms Reineke, often “forces people to choose between social death and the risk of physical death.”

Mexico may no longer be a big net exporter of people, but it is increasingly a transshipment point for migrants from Central America. A growing number of youths are fleeing crime and deprivation in countries such as Guatemala and, particularly, Honduras. Apprehensions of what the Border Patrol calls OTMs (“other than Mexicans”) grew from 51,000 in 2010 to 95,000 in 2012. The proportion of OTMs among the dead bodies identified by Ms Reineke’s project doubled between 2000-05 and 2006-12.

Even before they reach the border these migrants face dangerous conditions. Mexican authorities say that kidnappings of migrants have soared to around 20,000 a year. Organised criminals rob migrants on a terrifying cargo train known as La Bestia (The Beast), which travels from southern Mexico to the north, with migrants clinging to the roof. In May at least ten Hondurans were injured after criminals threw them off the train, reportedly for refusing to pay extortion money.

Most of America’s 2,000-mile southern border is tighter than it has ever been. Greater use of surveillance technology may reduce crossings further. Yet the growth in numbers from Central America shows how strong the “push” factors behind migration remain. America’s politicians may or may not find a way to declare the border “secure”. But if Mexico’s economy stutters, or violent crime soars again, the magnets of high wages, jobs and security across the border will prove too powerful for many to resist.

Correction: In an earlier version of this article we mis-spelled Jim Chilton’s name as Chiltern. Sorry.