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The Office of the Chief Actuary of the Social Security Administration, in an Apr. 2013 actuarial note, "Effects of Unauthorized Immigration on the Actuarial Status of the Social Security Trust Funds," available at ssa.gov, stated:

“While unauthorized immigrants worked and contributed as much as $13 billion in payroll taxes to the OASDI program [the Social Security trust funds] in 2010, only about $1 billion in benefit payments during 2010 are attributable to unauthorized work. Thus, we estimate that earnings by unauthorized immigrants result in a net positive effect on Social Security financial status generally, and that this effect contributed roughly $12 billion to the cash flow of the program for 2010. We estimate that future years will experience a continuation of this positive impact on the trust funds.”

Apr. 2013