The firms who do not win the visa lottery “just become smaller firms” instead of hiring market-rate labor because they still have to compete in a market against other firms who won the visa lottery and have access to below-market-rate labor.
Did the economists who ran this study miss this? Do they explain it?
I’d push back a bit on the idea that they simply missed it. They actually test something very close to this in the appendix: whether losing the lottery changes the competitive environment firms report facing. They don’t find a statistically significant competition effect
AEA leans strongly left. I wouldn't put much store in this.
Have you gotten a chance to read the paper? If not, you should consider reading it. They have explained it. It's got to do around the fact that domestic labor supply is inleastic but the foreign supply is infinitely elastic. You might want to focus on sections VI and VII for more details around their model and assumptions.