The effect of immigration on wages seems as if it must be obvious from Econ 101: increase the supply of something and you drive down its price. So immigration must reduce wages, right? The issues isn't that simple, for a number of reasons. Four such reasons are laid out by Giovanni Peri in "Immigration, Labor Markets, and Productivity." Peri points out that immigrant labor is often focused on providing home services, in a way that has tended to free up high-skilled native women to enter the workforce or to work more hours.
"In the United States (and in many European countries) one sector in which the presence of the foreign-born has been large and growing fast is that of home services (cleaning, food preparation, gardening, and similar) and personal services (child and elderly care). These are often characterized as “household production” services. This has allowed a significant share of female workers, often highly educated, to afford these services and to join the formal labor force outside the home or to increase their hours worked."
But even if low-skilled immigrant labor may be complementary to high-skilled native labor, surely it must depress wages of low-skilled native workers? Peri argues that this conclusion need not follow, because of ways in which firms and the economy respond to an influx of immigration. He writes (citations omitted): "In summary, an economy will respond to immigration along several margins—through increased investment by firms, specialization of natives, complementarities between natives and immigrants, technological response by firms, and job creation. ...This explains why a long tradition of empirical economic studies has found very small to no effect of U.S. immigration on native wages and employment at the national and at the local level."
Here is a bit more detail on each of Peri's four margins for economic adjustment in response to low-skilled immigration.
"As a consequence of the availability of more workers firms invest: existing firms expand their capacity, and new firms are born. Returns to capital increase when more workers are available, and firms take advantage of this by investing."
2) Differences among Workers: More and Less Educated
"Workers are not homogeneous. In terms of their labor market skills and productive activity there is a large difference between workers with high levels of schooling (tertiary education) and those with secondary or less. They use different skills and take different jobs. ... In the United States as a whole, however, because of the combination of immigrants at the top and at the bottom of the schooling distribution, if we consider two groups of workers (more and less educated), immigrants have a distribution similar to that of natives. Hence their inflow did not alter much the relative supply of the two groups."
3) Specialization and Technology: Job Upgrades
"Even more interesting is the differentiation of skills and productive characteristics between natives and immigrants within each of the two schooling groups. One very strong tendency among immigrant workers with low schooling is to concentrate in manual jobs. In manufacturing, construction and agriculture, for instance, they work as farm laborers, construction workers, roofers, drivers and so on. In services they work in food preparation, house services, child and elderly care. In contrast, similarly educated natives work in jobs which
use more intensively communication and interaction skills such as cooks, construction supervisors, farm coordinators, or clerks. In Peri and Sparber (2009) we show that, due to the limited knowledge of the language, immigrants have a comparative advantage in manual type of jobs. Hence they specialize in those, and in firms and sectors that hire immigrants, this produces higher demand for jobs of coordination and interaction typically staffed by natives, whose language skills are superior. This dynamic specialization in tasks according to skills pushes natives to upgrade their jobs (as communication-intensive occupations pay better than manual intensive ones) and protects their wages from competition with immigrants. By taking the manual jobs that natives progressively leave, immigrants often push a reorganization of production along specialization lines that may also increase effectiveness and efficiency of labor ... In some studies the mechanism described here, combined with the other effects described earlier in this section, results in a small positive effect of immigration on wages of less educated native workers."
4) Lower Wages of Immigrants: An Opportunity for Cost Cutting and Job Creation
"One common empirical finding in the literature is that immigrants are paid less than natives with similar characteristics and skills. This is in part due to the fact that many immigrants, because of less attractive outside options (such as having to go back to their home country), have lower bargaining power with the firm. In this case firms pay immigrants less than their marginal productivity, increasing the firms’ profits. Such cost-savings on immigrants act as an increase in productivity for firms. Ottaviano, Peri, and Wright (2010) show that if a firm can cut costs in some productive tasks by hiring immigrants, this allows the firm to expand production and employ more people in the complementary tasks, many of which are supplied by natives."
In short, the economy is not a static mechanism with a fixed number of jobs that require a predetermined set of skills. Instead, the number of jobs moves over time. Even among those with low skills as measured by education, there can be vast differentiation of skills between, say, those who are proficient in English and those who aren't. Low-skilled native workers can in many ways be complements with low-skilled immigrants, not substitutes. Firms can and do adjust their methods of production in many ways. An economy is a flexible organism. That flexibility can be difficult for workers, who need to change and adapt, and will sometimes find their old jobs altered or even ended. But the flexibility is also the source of a gradually rising standard of living over time.