True, there's not a one-to-one correlation, but there is definitely a causal relationship.
This article from the City Journal concludes that " Identity theft in America goes hand and hand with illegal immigration."
In 2007, one third of all consumer complaints received by the FTC were for identity theft. Most of these complaints were from illegal immigrant 'gateway' states - Arizona, California, and Texas, as well as Florida and Nevada.
Seeking access to jobs, credit, and driver’s licenses, many undocumented aliens are using the personal data of real Americans on forged documents. The immigrants’ identity theft has become so pervasive that the need to combat it is “a disturbing front in the war against illegal immigration,” according to U.S. Immigration and Customs Enforcement.
Since 2002, identity theft complaints to the FTC have increased by 60%! Identity theft is big business, and much of it is controlled by the latino gangs throughout the southwest U.S. of A.