As for the wider U.S. economy, experts said it is unlikely that Obama's executive actions will have a significant impact on employment or wages.
Citing the U.S. Immigration Reform and Control Act of 1986 that offered amnesty to about 2.7 million undocumented immigrants, Evercore concluded that research is mixed on employment-level changes (since many were already participating in the workforce), but that "most economists agree ... that new waves of immigration hurt previous immigrants."
"The literature is generally in agreement that the primary beneficiaries of legalization would be the eligible immigrants themselves, with the main benefit being an increase in earnings as workers formerly in the shadow labor market move to better, higher-paying jobs and earn greater returns on their educations," the Evercore note said.
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And while the real economy may not change much, investors should also not expect to see major moves in closely followed statistics, according to research from JPMorgan.
"We believe it will be hard to discern any large effects on the data," wrote Michael Feroli, the firm's chief U.S. economist, adding that "we think the labor market data are largely immune to changes in the legal status of workers."
Even the government's coffers—which would presumably benefit from more than 4 million expected new taxpayers—may not see a big bump from the president's actions. Many experts predict that about half of undocumented immigrants with jobs have false papers, so they are already paying taxes, said John Skrentny, director of the Center for Comparative Immigration Studies at the University of California, San Diego.