An Inconvenient Truth That Somehow Didn't Make The CEA Report

As I mentioned in a previous post, the CEA seems to have concluded that if one allows for complementarities between immigrants and natives who have the same education and work experience, the long-run gains from immigration are somewhere between $30 to $80 billion per year.

A careful reading, however, indicates that the CEA doesn't quite say that--and they are very careful about avoiding that particular terminology. Nevertheless, I think it is the “impression” one gets from the media coverage. Look at the headline at the MSNBC website: Immigrants 'Benefit US by $30bn'

I found that impression odd when I first saw the report, but I was in Spain at a conference and didn’t have the time to think it through. On the flight back, however, I took out a pad of paper and worked out the mathematical model.

As I suspected, the $80 billion number does not mean what most people would probably take it to mean. Economic theory predicts that the long-run gains from immigration to the pre-existing population must be zero—even when there are complementarities between immigrants and natives and even if those complementarities are incredibly strong. In the long run, capital adjusts fully until firms wither away all the excess profits from the initial wage depression. A short version of the mathematical proof is here, and here are more detailed handwritten_notes.

The CEA used the Ottaviano-Peri result that the complementarities helped natives and calculated how much natives gained as a result. This is what they say:

Multiplying the average percentage gains by the total wages of US natives suggests that annual wage gains from immigration are between $30 billion and $80 billion.

But they completely ignored the fact that the same complementarities that supposedly help natives also hurt immigrants, and by quite a bit. In other words, the CEA uses a strange definition of who “we” are: including only native-born workers and ignoring the millions of immigrants already here who are affected by yet more immigrants. This choice is not one that is typically made in the academic studies the CEA borrows from. In recent studies, the simulation usually examines the impact of a particular immigrant influx (say, the 1990-2000 arrivals) on the wage of workers present in the United States in 1990, regardless of where those workers were born.

Had the CEA taken the immigrant losses into account, the Bush administration would have had to report that the net gains from immigration for the pre-existing population are equal to.......ZERO!

And there's actually more embarrassing news, for a theorem is a powerful thing. Just for fun, let’s use a "CEA-approved" number for the native gain. The report is not very specific on how they get the $30-$80 billion range, so let's just pick $50 billion as the size of the long-run native gain. What does this $50 billion native gain imply about the size of the long-run losses suffered by pre-existing immigrants?

The economic theorem says that the average wage change in the population must be zero. Let's use the conveniently available CEA data: 15% of workers are immigrants and 85% are natives. If there were 100 million native workers, each native-born worker benefits by about $500 annually. If there were 15 million immigrant workers, each immigrant worker must lose $3,333 annually--and the $50 billion gain accruing to natives must be entirely offset by the $50 billion loss accruing to immigrants.

(A technical aside: the theorem says the weights to be used are income shares, and the share of immigrant income is smaller than their workforce share, so the correct weighting would lead to even bigger losses. Also, the weights should reflect the immigrant share in the pre-existing population--and again doing that would make the immigrant loss even bigger).

Imagine the headlines had the CEA reported that immigration during the 1990s led to a $3,333 drop in the average earnings of pre-existing immigrants! This is not the spin the White House was looking for, but it is a direct implication of the spin they did put out. What an inconvenient truth!

I wonder if the compassionate conservatives will shed a tear about the huge wage losses suffered by pre-existing immigrants.

UPDATE: The last four paragraphs have been edited to correct a misapplication of the theorem. (Thanks M.)

Comments

[CTL]

Thank you, Dr. Borjas, for keeping the light shining brightly on this issue.

[Ultima]

I have been unable to locate a source for your standard economic notation. Please define the notations used in your simple proof in your mathematical notes on CEA report. CES framework? etc.

[Ultima]

I often see the comment "most economists believe there is a net gain to the economy from the presence of illegal aliens." Is this true? Has there been any survey of a large number of economists? How does one answer such a claim?

[Ultima]

What are the long term implications of population growth due solely to immigrants, illegal aliens, their progeny and their higher fertility rates? Is it possible to achieve a soft landing for our economy with a stable population? Is a stable population a useful national goal?

Is it true that the limit of finite resources divided by population as the latter approaches infinity is zero?

[gborjas]

Ultima

Look at the derivation of the model in my paper that appeared in the Nov. 2003 issue of the Quarterly Journal of Economics. Everything should be clear once you go through that presentation.

[William]

It's interesting that many individuals and groups continue to ignore that the benefit of immigration is essentially economically insignificant.

Even the Heritage Foundation skips giving that mention in its recent piece on the CEA report. Although, I guess it shouldn't be a surprise that Heritage ignores this.

http://www.heritage.org/Research/Immigration/wm1524.cfm

By the way, this is a good blog Dr. Borjas. Thanks for taking the time out of your day to maintain it. Many of us listen closely to what you have to say and we appreciate you doing this.

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The only variable in comparing and contrasting immigrants to natives is that of culture, and because a great variety of immigrants demonstrate a widely varying set cultural capabilities, the study needs to evaluate discrete immigrant groups.
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