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Immigrants and Unskilled Workers: Complements or Substitutes?

Ezra Klein writes:

Ezra Klein: The Minimum Wage vs. Immigration: Giovanni Peri, who's actually conducted some of the research showing immigration has low wage suppression effects, explains his results this way:

On first thought, it might seem that the simple economics of supply and demand would answer the question: What is the effect of immigrants on wages? Immigrants increase the supply of labor. Hence, they should decrease the wages of native workers, reduce their employment opportunities, or push them to other states. The question, however, is more subtle than this, because all workers are not the same: They differ by education, skills, and occupation and perform jobs and productive tasks different from and complementary....

In nontechnical terms, the wages of native workers could increase because the increased supply of migrants is likely to put native workers in jobs where they perform supervisory, managerial, training, and in general interactive and coordinating tasks, which makes them more productive. Moreover, the presence of new workers also implies higher demand for consumption, so that immigration might simply increase total production and demand without depressing wages...

Giovanni's arguments do seem to make sense of the data from immigrant-rich California. My guess is that complement and substitute effects more-or-less cancel each other out, but it's only a guess.