WSJ: THE NUMBERS GUY

Fuzzy Math on Illegal Immigration

THE NUMBERS GUY

By CARL BIALIK

April 5, 2006

New York Democrat Charles Schumer said legislation is needed "to solve the problem of millions of foreigners who live here illegally and unprotected" as well as "to alleviate the problem of the millions more who enter illegally every year." He kept his estimate of the number of illegal immigrants vague because "no one knows for sure how many are really here," the National Journal reported. "Nor can anyone give a reliable estimate of how fast that unknown figure is growing each year."

A sound bite from last week? Nope. The year was 1985, Mr. Schumer was in the House of Representatives and debate was raging over how to address the growing number of illegal immigrants, then estimated at somewhere between 3 million and 12 million.

Twenty-one years later, several amnesties granted to undocumented immigrants have failed to keep the number of illegal immigrants from growing. And estimates of their numbers remain fuzzy and full of pitfalls, even as lawmakers toss them around in the latest round of debates over whether to offer guest-worker status to illegal immigrants.

At the core of the problem is the fact that undocumented immigrants don't generally come forward to be counted. The most widely quoted estimate of 11 million to 12 million is derived indirectly, using what's called a residual method: Researchers subtract the number of immigrants who were authorized to come to the U.S. from the number of foreign-born residents counted by the Census Bureau, then adjust the number using estimates of immigrants' deaths and migration, and of Census undercounting. Some critics say that estimate understates the degree of undercounting: Another estimate making the rounds holds that there are 20 million illegal immigrants.

That was the upper range Bear Stearns analysts Robert Justice and Betty Ng estimated last year, citing high growth rates in foreign remittances and in school enrollments in localities with high illegal-immigrant populations. The analysts added, "According to our discussions with illegal immigrants, they avoid responding to census questionnaires."

And there are still-higher estimates to be found online: The Web site of the "immigration crime-fighting" group American Resistance Foundation estimates there are more than 28 million illegal immigrants, based largely on border-patrol apprehension rates; however, there is little reliable data on how many border-crossers who are caught trying to enter a second time.

"No one really knows," says Bill Strassberger, a spokesman for the U.S. Citizenship and Immigration Services, a branch of the Department of Homeland Security.

Of those citing the 20 million figure, Mr. Strassberger says that "the number seems to be agenda-driven." But if so, it's not always the same agenda doing the driving.

On CNN last Sunday, anchor Lou Dobbs, who has argued for tighter border controls, spoke of "the toll that 20 million illegal aliens take on the infrastructure of the United States and on local, state, and federal taxpayer budgets." (At other times during his recent broadcasts, Mr. Dobbs has cited a range between 11 million and 20 million. A CNN spokeswoman says Mr. Dobbs is relying on the Bear Stearns report for the higher number.)

But talk-show host Tony Snow, arguing that immigrants are a boon to the economy, wrote Monday, "The United States somehow has managed to absorb 10 million to 20 million illegal immigrants not only without turning into Animal Farm, but while cranking up the most impressive economic recovery in two decades."

In 2000, before it was folded into DHS, the Immigration and Naturalization Service used the residual method to estimate there were seven million illegal immigrants and their numbers were growing by 250,000 to 300,000 per year. Mr. Strassberger says that remains the government's best estimate, though he concedes it's out of date.

Following largely the same procedure that INS used, the Washington, D.C., think tank Pew Hispanic Center counted 11 million illegal immigrants last year, and between 11.5 million and 12 million last month; the group is the source for most lawmakers and reporters citing a number. (The Wall Street Journal generally has printed estimates of 11 million, or a range of 11 million to 12 million.)

But the residual method is by necessity complicated, and each step in its formula introduces uncertainty. Jeffrey Passel, a Pew senior research associate, walked me through the procedure (also outlined in Pew's latest report). The starting point is the Census Bureau's annual Current Population Survey report, which bases a count of foreign-born residents on interviews conducted with about 80,000 households. The Census intentionally seeks out a disproportionately large number of Hispanic households to get richer data. Interviewers, either by telephone or in person, ask where every member of each household was born. These figures are then extrapolated to the nation, adjusting for the larger sample of Hispanics. The latest estimate of foreign-born Americans to emerge from such calculations was roughly 36 million, Dr. Passel says.

Next, Pew subtracts the number of foreign-born Americans authorized to be in the country. Dr. Passel's team compiles annual numbers of green-card recipients, refugees and people granted asylum, a count that stretches back decades. But merely adding these numbers would be misleading, because some authorized immigrants decide to leave the country and others die. Dr. Passel assumes that immigrants of a certain age die at the same rate as the country's residents overall, and uses estimates from various studies on "outmigration," something he concedes is "hard to measure." (The outmigration numbers are also much bigger -- perhaps seven times as large -- as the number of deaths, because immigrants tend to be young.) Then the calculated total is subtracted from the total number of foreign-born residents, and the result is adjusted upwards by 10% to account for census undercounting of illegal immigrants. (That adjustment is based on one post-Census 2000 survey of undercounting among Mexican immigrants in the Los Angeles-area; other studies have yielded different estimates of undercounting.)

Dr. Passel and Robert Warren pioneered the residual method while working together at the Census Bureau in the 1980s. Dr. Warren then helped develop INS's methods for its 2000 estimate, so it's no surprise that the government's methods are similar to Pew's. Michael Hoefer, director of the office of immigration statistics, a branch of DHS, told me that the government uses the Census Bureau's American Community Survey instead of the Current Population Survey, which is based on a larger sample of households but is published later than the CPS. (Mr. Hoefer's office is working on a 2004 estimate to update the 2000 official figure of seven million.)

Also, Pew's count of illegal immigrants includes those considered "quasi-legal," meaning they're on their way to legal status, and awaiting asylum or in temporary protected status; INS's count doesn't, though the next round of government estimates might. That could mean a difference of about one million in the total count, Mr. Hoefer says.

Back in 1985, Dr. Passel told the National Journal, "The fatal flaw in virtually every study was that there's some assumption that you have to make in your estimation model for which there is absolutely no data." But he says now that estimation methods have improved, thanks to refinements of the residual-method technique, more-regular Census counts of the foreign-born population, and comparison of the numbers with Mexico population figures to see if the estimate of illegal immigrants from Mexico squares with a gap between expected and actual population counts south of the border.

However, there is still large uncertainty in the current estimates, due largely to Census undercounting and limited data about immigrants leaving the country. It's impossible to say how uncertain the estimates are; neither Pew nor the government publishes a margin of error, which is a standard component of most statistical estimates.

The variable numbers have provided material for Comedy Central's Stephen Colbert, who noted that on a recent Sunday political talk-show, Sen. Arlen Specter, a Pennsylvania Republican, referred to "11 million undocumented aliens," and just 30 minutes later on a different network, Massachusetts Democrat Ted Kennedy used the "12 million figure." Mr. Colbert's comment: "One million illegals snuck into this country in half an hour! That is alarming. At that rate the entire population of Mexico would be here in three days. Congress, get to work on that fence." Mr. Kennedy's spokesman cited the Pew report; a representative for Mr. Specter didn't return my call seeking comment. (Numbers Guy readers Allen Cantrell, Shauna Laughna and Robert Tamiso also spotted inconsistent immigration numbers and suggested this column topic.)

Not everyone agrees that the numbers debate matters. "As long as people concede that the number is large to begin with and is increasing, the number itself is irrelevant," Vernon Briggs, a professor of labor economics at Cornell who favors enforcing sanctions against employers of illegal immigrants, told me.

But if that were so, the numbers wouldn't be continually cited by lawmakers and the press, who would serve their constituents and audience better by acknowledging the uncertainty of these estimates.

* * *

Several readers wrote in about my column last week on the different naming schemes world-wide for large numbers, and the efforts of Swedish scientist Anders Thor and others to standardize things. Here are excerpts from letters:

Mr. Thor has a unique window of opportunity to rally the U.S. into switching to the European methods of measuring large numbers -- it would immediately reduce the U.S. budget deficit.

--Judy Sterling

I've been waiting for someone to write this for some time. I've lived in Spain and it always fascinated me how people would say Mil Milones -- this was rather common as well when speaking of money prior to the Peseta/Euro change over.

--Patrick J. Sullivan, CFA

I enjoyed your column. It reminded me of a consulting project I worked on several years ago in Bangladesh. The Bangladeshis used their customary units of lakh (10,000) and crore (10 million) in budgets and other reports involving large numbers. At the time their currency, the Taka, was worth about two cents, so there were plenty of big numbers. To make matters more confusing (to us Americans anyway), lakh and crore numbers have digits grouped by twos, instead of threes. When looking at lakhs or crores, you'd have to suppress all your instincts to come up with the right value. Reports from most international agencies followed American number conventions, but the convention wasn't always clear in some European sources. It made for plenty of confusion. My suggestion for clearing up this mess: Let's all switch to using scientific notation.

--Charles Hartel

I second Charles's suggestion, and expect it to happen soon after we all switch to the metric system. Those unfamiliar with the lakh-crore system, and the two-digit groupings, can learn more at Wikipedia.

I have to ask how you came up with the "28.5 trillion brackets per second" in the 90 hours to achieve the perfect NCAA bracket. I trust you are correct, but could you explain the method?

--Jason Maus

Here's my method: There were 32 first-round games, each of which could have two possible outcomes, so the number of ways to fill out the first round of the bracket is 2 to the 32nd power, or 4.3 billion (following the U.S. definition for billion, as explained in last week's column). For each of those permutations, there are two possible winners in each of the 16 second-round games, so you'd have to multiply 4.3 billion by 2 to the 16th power, or 65,536. Follow that logic through to the championship, and you'll find there are 2 to the 63rd power -- or 9.22 million trillion -- possible brackets. There are 324,000 seconds in 90 hours, so divide that into 9.22 million trillion and you get 28.5 trillion brackets per second.