Gross Nets and Illegal Immigrants

Some More Thoughts

I am unable to let an issue rest.

Noah has a response to my critique of his claim that “illegal immigration has been zero/negative”. I am very motivated to see this thing through to its conclusion, so let’s review where we are.

1. Noah explicitly referred to a graph labelled “Annual change in unauthorized immigrant population.” as showing that about a million undocumented immigrants left the country over the period in question, indicating he views net change as the correct proxy for net migration, without need for adjustment. This remains the text as it stands to today, that is, no revision has been made. Elsewhere in the post, Noah refers to the graph as showing “net international migration” despite the fact that it definitely does not show net international migration. The label even says it doesn’t show net international migration. It’s just change. Lyman- 1, Noah-0.
2. Noah argues that I misinterpret the margins of error for changes between year. I‘m not totally convinced, but I’m not interested in the fight. I wish he’d do the work himself and show what the error bars should be as he views it, and then add them to his post, or at least make a footnote on the graph. I’ll concede here and say, sure, maybe I was not correct in simply taking the min-max possibility for each year and subtracting. Conceded. Lyman-1, Noah-1.
3. Noah explicitly states that he forgot to include mortality. He finds a paper that estimates it in a range pretty similar to the range I guessed at. Calculating it out, he estimates 264,000 deaths from 2009–2014, 347,000 from 2007–2014. I originally guesstimated 264,000–408,000 for 2007–2014, and 207,000–307,000. So his final estimates were comfortably near the midpoint of the range I gave. Recall, Noah’s original estimate of mortality was implicitly zero: he forgot to include it, and called all net change net migration. So this makes Lyman-2, Noah-1.
4. Let’s keep harping on mortality. Noah finds that when you look at net change from 2009–2014, the postrecession period he’s mostly concerned about, adjusting for mortality yields net changes due to migration at positive 64,000! In other words, far from being zero/negative, when you adjust for mortality using the method Noah prefers, you get positive net migration into the use among undocumented residents. Given that Noah’s claim was zero/negative, and given his mortality estimate comes from a period when the undocumented resident population was substantially younger so real mortality post-2010 was probably higher, this suggests excluding mortality actually changes the meaning of the data. In other words, Lyman- 3, Noah- 1.
5. Noah says I’m ignoring the obvious; clearly nobody would interpret his comments as being about gross migration. I disagree, I think headlines matter quite a bit. And given that one side of the political debate cares a lot about border control, seems like Noah should care about gross flows. If his goal is to write exclusively for people who are totally apathetic about gross flows, then okay, but my understanding is Noah wants to persuade people of his views, and simply defining half the political spectrum out of existence by insisting that gross flows are irrelevant seems odd. Nonetheless, I grant that any considerate reader would come to realize Noah meant net flows despite saying gross flows. Lyman-3, Noah-2.
6. But what’s weird is Noah then gives good reasons why gross flows really do matter. He suggests that churn can alter the pace of assimilation and various other factors, which, to me, seems like game-set-match. The pace of assimilation is the most important factor as far as immigration restrictionists are concerned. Don’t believe me? Read the most articulate restrictionist out there, Paul Collier, and his book “Exodus.” Really, assimilation pace is the entire game. So I’m gonna go ahead and say Noah’s concession that churn has a substantive role in defining the pace of assimilation is an important concession; i.e. nets aren’t all that matter. Lyman-4, Noah-2.
7. Noah makes a fair point: as far as the major demands on the labor market and government go, stocks do matter more than flows. He’s right about that. I never disputed it the view that stocks were of great importance, but nonetheless, credit where credit is due. Lyman-4, Noah-3.
8. But this is odd, since Noah presented flows data, not stocks data. His flows data visually portray big changes, while the stocks data show small changes. Showing net change data is visually equivalent to truncating the Y-axis by a fairly extreme amount. Most people would recognize that so truncating the Y-axis is improper data visualization when recent history has values far outside the truncation. i.e. Noah implicitly is displaying a graph of the undocumented stock, truncated at about 11 million people, despite very recent history below 11 million. That’s what the annual change data is showing. That doesn’t seem proper to me, given many of these YoY changes are not statistically significant, according to Pew. Improper dataviz is a capital crime, therefore, Lyman-5, Noah-3.
9. But here’s the rub on why we really shouldn’t show this annual data. Noah’s view is that annual estimates of illegal immigration are statistically unbiased… but that’s not true. I outlined several sources of almost-guaranteed statistical bias: the fixed outflow rate of permanent residents, cyclical category changes due to benefit classifications, volatility in temporary residents, the rounding not adding up to zero across a small number of years, etc. Noah’s problem is he wrongly believes that Pew estimates the unauthorized resident population from some random survey of them. They don’t! You can’t reasonably apply statistical tools designed for a (pseudo)random sample to estimates that fall out the back-end of a fairly complex process involved some very non random sample inputs, like the estimation of the permanent and temporary resident populations. The statistical error of the ACS enters the calculations via both the core estimates that Pew reports, but also DHS’ use of ACS estimates in their permanent resident calculations (not adjusted by Pew). Non-ACS error enters the calculations through the LPR and LTR channels as well. And of course, while it’s certain that ACS does not cover all undocumented immigrants, it is not certain, as Noah suggests, that errors are serially correlated. i.e. it’s reasonable to think changing legal and economic conditions, as well as random idiosyncracies, could cause fairly large and random changes in what groups response to the ACS (especially since ACS response rates are falling overall). Given all these factors, there’s a very good reason that Pew doesn’t typically highlight YoY change in this data. It’s best to stick with differences in fairly distant points, and avoid being too specific. In other words, Lyman-6, Noah-3.

But, to repeat, there’s just no reason for this debate. Just change the graph and a handful of phrases. Here’s the unauthorized immigrant share of the population, 1990–2016, according to Pew (no error bars because I didn’t know where to find them; maybe Noah can; but errors are larger in 2015/2016):

See? This graph is nice. It makes the point even better than Noah’s original graph, it’s less noisy, and it’s far more justifiable. Add an error band and you’d be golden.

Because if you want to talk about sources of change, it gets tricky. So, for example, we can get estimates of mortality among undocumented residents. We can also guesstimate inflows by looking at apprehensions and making a simplifying assumption that immigration probably has a similar trend. With those two factors in, the residual is probably emigration. So, for example, let’s assume border control apprehends or denies admission to 50% of the people who attempt entry into the U.S. and would be included in the undocumented population. In other words, assume apprehensions/denials of admission along the SW border are 1 1-to-1 proxy for inflows. It’s a rough sketch, but alas, it’s what we’ve got. Don’t see these estimates as proof that something must be the case, see them as evidence that we cannot rule out, as of now, certain things being the case.

Furthermore, I have more recent data than Noah. He published in February. Since then Pew has released the 2015 ACS estimates, and preliminary 2016 ACS estimates. Here are the estimates for components of change from this calculation:

As you can see, emigration/immigration are individually waaaaaaaaay bigger than mortality. But mortality is of a similar scale to net migration! In other words, comparing mortality to emigration looks small. But comparing across-period mortality to net migration looks rather striking.

You’ll note that two bars (actually 3, but the last bar for net migration is very close to zero by coincidence) are positive for net migration, meaning from for that period, there was more illegal immigration than emigration of unauthorized residents. That’s for 2007–2016 and especially 2009–2016. However, I specify these periods twice. The ones showing positive net migration are the midpoint of Pew’s 2016 estimate, which is based on the CPS, not the ACS. This estimate showed a visible uptick in the population in 2016. However, it has a very wide error band, and is not statistically different from 2015. So I also show a 2007–2016 specification where I use the low end of the CPS-based population estimate range. By this calculation, net migration is still zero.

But the point is, estimating net migration is very sensitive to the time period you select, your assumptions about mortality, and your assumptions about the time-path of immigration.

For all these reasons, it’s a very bad idea to try and make strong assertions about specific population change components for unauthorized residents the centerpiece of political commentary. We actually cannot rule out continuing positive migration through 2016 at least, and even for 2014 In other words, Lyman-7, Noah-3.

This all comes down to the problem I highlighted in the last post: the pretense of knowledge. Commentators are under pressure to produce material, and material with a takeaway to it, material that conveys authority. As such they reach for authoritative data and information where, in fact, there are few or no powerful indicators. They make claims far beyond what the evidence can bear. And even if the over-arching argument is correct (Noah’s pretty much is), by leaning on bad evidence, they make the correct argument look unconvincing. My dad, who is a Bible translator and commentator, has a saying that often pastors teach “The truth, but not the text.” That is, they may be arriving at a correct place despite terribly misreading the evidence. That’s what I think has happened here, and I do hope Noah will make the fairly-small fixes necessary to alleviate the problem.

PS — If stocks are what matter, and stocks have not declined very much from their record high levels, then isn’t the implication of the “stocks not flows!” line of argument that illegal immigration remains near its greatest levels of urgency ever? Lyman-53,618, Noah-3

Check out my Podcast about the history of American migration.

If you like this post and want to see more research like it, I’d love for you to share it on Twitter or Facebook. Or, just as valuable for me, you can click the recommend button at the bottom of the page. Thanks!

Follow me on Twitter to keep up with what I’m writing and reading. Follow my Medium Collection at In a State of Migration if you want updates when I write new posts. And if you’re writing about migration too, feel free to submit a post to the collection!

I’m a native of Wilmore, Kentucky, a graduate of Transylvania University, and also the George Washington University’s Elliott School. My real job is as an economist at USDA’s Foreign Agricultural Service, where I analyze and forecast cotton market conditions. I’m married to a kickass Kentucky woman named Ruth.

My posts are not endorsed by and do not in any way represent the opinions of the United States government or any branch, department, agency, or division of it. My writing represents exclusively my own opinions. I did not receive any financial support or remuneration from any party for this research.