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Friday, June 22, 2007

Who Are "We"?

George Borjas says recent says a recent CEA report left a misleading impression about the benefits from immigration by using a non-standard assumption of who ought to count in the calculations when tallying up gains and losses. When a broader definition of "we" is adopted, and when theoretical results about the long-run impact of immigration are imposed, a different interpretation can be placed on the results in the report:

An Inconvenient Truth That Somehow Didn't Make The CEA Report, by George Borjas: 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, ...[so] 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.

Borjas62207

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...

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?

[see correction below] 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 the 85% get a gain of $50 billion, then the remaining 15% must have suffered a loss of $280 billion to make the theorem hold up!

(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 $280 billion loss for 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: Brad DeLong has more comments. He says:

George Borjas appears to get the economic theory not quite right...

Update: George Borjas says "Update: The last four paragraphs have been edited to correct a misapplication of the theorem. (Thanks M.)" This correction was done before Brad's post above (which refers to the corrected version):

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: George Borjas responds to Brad DeLong:

DeLong On Immigration, by George Borjas: Brad DeLong has jumped into the discussion of what economic theory has to say about the long-run gains from immigration to the pre-existing population. ... This is DeLong's reaction:

Now that's simply wrong: "capital adjusts fully" means that more future investments are made in high-productivity areas to which migrants move and fewer in low-productivity areas from which migrants came. Returns on savings are thus higher--and because the pre-existing population are savers, they benefit. So do the migrants.

Soon after DeLong's blog post appeared, my colleague Dani Rodrik emailed me:

I assume the model you have in mind is one where capital is internationally mobile, and the US is relatively small so that the return to capital is fixed in the long run. So when workers come in, there is a short run increase in r, which is dissipated over time as foreign capital moves in. In the end, all natives have same welfare, while the migrants are better off. That in any case is the simplest model in which you are right and Brad is unjustified to say you are wrong, is that the story?

Yes, Dani, that is exactly the story. DeLong is just plain wrong within the context of this model. Perhaps DeLong has a different model in mind. But whatever model he has in mind is not the model that was the basis for the CEA estimates. The underlying model in the CEA calculations defines the long run counterfactual exactly as Dani succintly summarized in his email.

UPDATE: I should have defined the variable r in Dani Rodrik's email; it gives the rate of return to capital.

    Posted by on Friday, June 22, 2007 at 12:15 AM in Economics, Immigration, Politics | Permalink  TrackBack (0)  Comments (9)

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