Behind the Pew Study on Illegal Immigration, Part III: Estimating Illegal Immigration - The Basic Model and Its Limitations

The basic approach of both the recent Pew report and those of the Department of Homeland Security in estimating the number of illegal immigrants currently in the United States is based on the "residual method" and seems, on first glance to be quite straightforward.

Pew describes this process as follows: "a demographic estimate of the legal foreign-born population – naturalized citizens, legal permanent residents, temporary legal residents, and refugees – is subtracted from the total foreign-born population. The remainder, or residual is the source of the population estimates and characteristics of unauthorized immigrants." (p. v, emphasis added)

It sounds simple, but it is anything but.

The first important thing to keep in mind is a point made by Pew’s chief demographer Jeffrey Passel in an earlier Pew study, "Because of inherent uncertainties in the residual technique, the difference in successive annual estimates of the unauthorized population is not a valid measure of growth" (p. 10, emphasis added). In other words, one of the two senior authors of the current study is already on record as cautioning against taking these (and his) estimates as validated real numbers.

One reason for this is that the amount of illegal immigration is very difficult to know because it is illegal and the consequences for those discovered to be so are dire. Dr. John Salt, head of the Migration Research United At University College London, testifying before a Select Committee of the United Kingdom's House of Lords on the Economic Impact of Immigration, said point blank "no satisfactory method of counting the illegal population."

The reason for this statement becomes instantly clear when you realize the immigrants both come and go and yet the Unites States has no measure of how many immigrants ever leave the country. As a 2009 New York Times article put it, "Eight years after the Sept. 11 terrorist attacks and despite repeated mandates from Congress, the United States still has no reliable system for verifying that foreign visitors have left the country." There are also no reliable figures for reverse southern border crossings. The DHS analysis says of this (p. 7, emphasis added), "Emigration is a major component of immigrant population change. In the absence of data that directly measure emigration from the United States, researchers have developed indirect estimates based largely on Census data."

So too, illegal immigrants age and die. However, the DHS analysis says (p. 6, emphasis mine), "Data are not collected on the mortality of legally resident immigrants" and this is obviously true as well for illegal immigrants. As elsewhere, estimates are made.

The basic numbers of persons and immigrants in the general population for the DHS estimates are gathered from the American Community Survey, a nationwide sample survey of about 3 million households. The Pew survey draws its figures from the Current Population Survey "of about 55,000 households." Clearly a sample of 3 million households will be more accurate than a sample of 55,000, but all the samples apply statistical enhancers (weighting and reweighting) for underreporting and estimates of a range to take into account over reporting.

Deep in the Pew report section on methodology we find the following disclosures:

1. "that the 2007 and 2008 population estimates from the Census Bureau made significant changes in the methodology used to measure internal migration from 2000 onwards." (p. 24)

2. "…in the 2007 and 2008 population estimates, the Census Bureau made significant changes in the methodology used to measure international migration from 2000 onward." The changes "are concentrated in groups where a high percentage of the population is foreign born, notably working-age Hispanics and Asians. As such the new population controls have the potential for affecting the measured size of the foreign-born population." (pp. 24-25, emphasis added)

3. "Although the changes caused by reweighting [the original data from the Census Department that Pew used], their impact can be relatively greater on the residual estimates of unauthorized immigrants." (p. 25, emphasis added)

And after all of these disclaimers comes the critical punch line.

4. These methodological changes led to a reduction of about 1.1 million in the estimated population for March 2007 between the Vintage 2006 estimates [monthly estimates used to estimate population figures for the next year] and the Vintage 2008 estimates. Although this change represented only about 0.4% of the U.S. population, it was concentrated in the Hispanic and Asian populations because immigration plays such a large role in these groups. The differences were further concentrated in the adult age groups so that the impact on the Hispanic population was about 1.5%, with some age groups being more than 2% smaller in the Vintage 2008 population estimate than the previous one. As a result, there is a major discontinuity between CPS [Current Population Survey] results for 2007 and earlier compared with 2008 and later." (p. 25, emphasis added)

Allow me to translate. Counting the total number of foreign-born persons and subtracting the number of naturalized citizens, legal permanent residents, and refugees, obtain the total number of illegal immigrants in the United States. Since there is no actual count for any of these figures, statistical estimates are used and these need to be artificially weighted by further estimates of the size of the different categories that make up the total (e.g., estimates of when the immigrants arrived, their age, and so on).

A real figure for the number of illegal immigrants would take into account how many leave the United States in any year. This figure would be particularly important in knowing how many illegal immigrants might be responding to changes in economic circumstances or enforcement. No figures whatsoever are available for these numbers, nonetheless they are estimated. So are the number of immigrants who die each year, another element in overall assessment of the number of total legal and illegal immigrant categories that make up the Pew and U.S. government estimates.

Furthermore, changes in the calculation of estimates by the federal government of the legal and illegal population necessitated "reweighting" of the original estimates used by Pew for their estimates. This "reweighting" has a particularly pronounced effect on the estimates of Hispanic and Asian groups, and even more of an effect on adult age groups, those most likely to be in work force either legally or illegally.

Each of these weighting exercises carries with it the risk of over- or underestimating the real numbers, and thus they carry a "confidence level" that the estimated results are in a particular range. The higher the confidence level figures the more likely the estimated numbers are within the range that that estimates estimate.

These changes in how the estimates are calculated, to repeat, "led to a reduction of about 1.1 million in the estimated population for March 2007 between the Vintage 2006 estimates and the Vintage 2008 estimates."

Assuming that the recalculation revisions are correct, at least part of the overall reduction in the estimated number of illegal immigrants that Pew reports is itself a byproduct of that recalculation.

What is the real number of illegal immigrants in the United States and how much has the population of illegal immigrants been reduced in the last few years for whatever reason?

The truthful answer is that no one can say for sure, and the numbers that are taken as authoritative may be, but are themselves sample estimates recalculated on the basis of further estimates which have added to them estimates of factors that effect them for which there are no actual numbers of any kind.

Caveat perscriptor.