Unauthorized and low skilled immigrants are attracted to America’s labor markets, not the size of welfare benefits.  From 2003 through 2012, many unauthorized immigrants were attracted to work in the housing market.  Housing starts demanded a large number of workers fill those jobs.  As many as 27 percent of them were unauthorized immigrants in some states.  Additionally, jobs that indirectly supported the construction of new houses also attracted many lower skilled immigrant workers.

Apprehensions of illegal crossers on the Southwest border (SWB) is a good indication of the size of the unauthorized immigrant flow into the United States.  The chart below shows apprehensions on the SWB and housing starts in each quarter:

Fewer housing starts create fewer construction jobs that attract fewer crossings and, therefore, fewer SWB apprehensions.  The correlation holds before and after the mid-2006 housing collapse. 

What about welfare? 

Here is a chart of the national real average TANF benefit level per family of three from 2003 to 2011 (2012 data is unavailable) and SWB apprehensions:

Prior to mid-2006, TANF benefit levels fell while unauthorized immigration rose.  During the housing construction boom, unauthorized immigrants were attracted by jobs and not declining TANF benefits.  After mid-2006, when housing starts began falling dramatically, real TANF benefit levels and unauthorized immigration both fell at the same time.  If unauthorized immigration was primarily incentivized by the real value of welfare benefits, it would have fallen continuously since 2003.   

The above chart does not capture the full size of welfare benefits or how rapidly other welfare programs increased beginning in 2008.  As economist Casey Mulligan explained in his book The Redistribution Recession, unemployment insurance, food stamps (SNAP), and Medicaid benefits increased in value and duration beginning in mid-2008.  Including those would skew welfare benefits upward in 2008 and beyond, but unauthorized immigration inflows still fell during that time.

In conclusion, housing starts incentivize unauthorized immigration while TANF does not.