It seems obvious to me that fewer low skill workers would result in higher wages for those who could most benefit from it.
Here's one classic study on the effect:
David Card, "The Impact of the Mariel Boatlift on the Miami Labor Market" (1990), http://davidcard.berkeley.edu/papers/mariel-impact.pdf
Quoting from the abstract: "…This paper describes the effect of the Mariel Boatlift of 1980 on the Miami labor market. The Mariel immigrants increased the Miami labor force by 7%, and the percentage increase in labor supply to less-skilled occupations and industries was even greater because most of the immigrants were relatively unskilled. Nevertheless, the Mariel influx appears to have had virtually no effect on the wages or unemployment rates of less-skilled workers…"
That's a rapid influx of 7% of Miami's population! But the effect isn't obvious to economists, either, and you can find people arguing both sides. This is a fairly balanced article: https://www.npr.org/2017/08/04/541321716/fact-check-have-low...
You would think that two income earners in a household would increase the economy enough that wages would need to rise due to a subsequent shortage of labor... but it did not.
Wages, in real terms, have largely lost purchasing power to the point where it takes two incomes to have the same (or less) purchasing power than one income did prior to WWII.
Part of it is the productivity gains made post WWII (i.e. we can do more with less labor) but a lot of it is the supply side of labor and competitive pressures pushing the price equilibrium (wages) down.
I'm not making an argument against the entry of women into the workforce. I'm an advocate for 'freedom' so I'm all for women doing what they want as long as they are following the law. My point here is the supply side of labor does not have a large enough increase to the demand side of labor to make up for the decrease in the price of wages.
The argument I am arguing against is something like:
Immigrants join the labor force -> They increase the economy -> The increase in the economy increases jobs -> More jobs increase wages.
I think this what you are essentially saying?
The problem here is inflation and productivity. In order for everyone to prosper either:
1. There is no inflation and therefore purchasing power is maintained, or
2. Wage growth and interest rates outpace inflation.
No. 1 will not happen under our current monetary system, and no. 2 has not happened due to:
a) Competition in the labor market has keep real wage growth flat, and
b) The unprecedented (in the history of mankind) money creation (AKA Quantitative Easing) used to bail out financial institutions has destroyed interest rates and created a massive inflation in asset prices.
Another factor is that different jobs impact the economy differently. Or put another way, different jobs create different levels of 'value' in society (the monetary kind not moral kind). The difference between the price of a good or service, and the perceived value of a good or service is the 'consumer surplus'.
Fact is, highly skilled immigration is going to create a higher level of consumer surplus compared to low skilled immigration. Highly skilled immigration in areas where there are shortages is going to also have a bigger impact on economic growth.
I think you will be hard pressed to find anyone arguing against this sort of immigration... the issue that dare not be spoken is the impact low skilled and illegal immigration has on the labor market.