I am not sure what legal status means in this paper.
If it means you can lose legal status if you commit crime subsequent to acquiring it, that means that the punishment for the crime is great and so we see less crime.
Legal status may also mean that your opportunities for legal ways of obtaining income a greater. The opportunity cost of crime is greater because the rewards have fallen relative to a legitimate job.
The opportunity cost of moving between the illegal workers market and criminality is less than moving between the legal labour market straight over into criminality .
Cool study forthcoming in AEJ Applied about how legal immigration status reduced recidivism of foreign prisoners in the EU. Here’s a link to an un-gated version of the paper.
Here’s the abstract:
We exploit exogenous variation in legal status following the Jan- uary 2007 European Union enlargement to estimate its effect on immigrant crime. We difference out unobserved time-varying fac- tors by i) comparing recidivism rates of immigrants from the “new” and “candidate” member countries; and ii) using arrest data on foreign detainees released upon a mass clemency that occurred in Italy in August 2006. The timing of the two events allows us to setup a difference-in-differences strategy. Legal status leads to a 50 percent reduction in recidivism, and explains one-half to two-thirds of the observed differences in crime rates between legal and illegal immigrants.
So the good news is that the identification scheme here is pretty darn good. The…
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Utopia, you are standing in it! 
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