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Suppose an Indian programmer that in India gets $20K a year moves to the US where he gets $80K for a job for which the natives get $120K. Now you allow him to change jobs. There are only two possibilities:

1) There is a company that would be willing to hire him for $120K.
2) There is no a company that would be willing to hire him for $120K. In this case he either stays with his original job or moves to job which offers him a more modest salary raise.

In no case would he move back to India to the $20K salary.






Letting immigrants change jobs changes the incentives. If the immigrant can change jobs and therefore has to be paid a market salary ($120K in your example), the company would never sponsor him for immigration in the first place because the company can no longer profit from paying him a below market salary.
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