Actually some statistics I have read indicate the second, third and subsequent generations are more prone to crime because of lack of fully assimilating into our society.
Between the foreign-born generation and their American children, the incarceration rate of Mexican-Americans jumps more than eightfold, resulting in an incarceration rate that is 3.45 times higher than that of whites, according to an analysis of 2000 census data by the pro-immigrant Migration Policy Institute.
http://www.city-journal.org/html/16_3_immigration_reform.html