Causal inference has progressed a lot since their paper.
[0] https://projecteuclid.org/journals/statistical-science/volum...
Many, many economists cite this study to say that immigration doesn't reduce wages. And it is true, often. However it's not because an influx of workers doesn't create downward pressure on wages. It's because there's other factors which keep wages rising.
Now in Canada we have a situation where our immigration levels are so high that we don't even pretend it doesn't affect wages anymore.
https://www.baystreet.ca/economiccommentary/3472/Canada-Wage... https://financialpost.com/news/economy/immigrant-influx-is-s... https://www.bloomberg.com/news/articles/2021-11-24/immigrant...
So one of the main theories about that paper is that the immigrants were in a largely separate labor market in terms of skills/experience from local workers. When they raised the labor supply in their particular market, it increased entreprenurial activity and more labor was hired across many labor markets as a result.
For example, they say immigration doesn't affect wages. In Canada our government and top banks literally all say it does. There's also a wide body of evidence that increased labour supply does put downward pressure on wages (now whether they actually fall or stagnate depends on a combination of other factors).
Card/Krueger's work is like perfectly fitting a regression line to historical data. It has predictive power until it doesn't...