Cato loves to lie, it seems. They have a study showing that "illegal immigrants commit less crime than citizens." First, they commit more crime than legal immigrants (ignoring the initial crime of coming here illegally, which would put the illegal immigrant pool at a staggering 100% criminality rate). This suggests that the immigration process does work to filter out some of the criminal element. If we have a process that reduces crime among immigrants, namely the legal immigration process, it seems like special pleading to suggest that we should remove that process simply because we have a pre-existing crime problem: If we suddenly solved inner city crime, and brought it down to the rate we see in suburban and rural communities, I doubt Cato would then reverse their position. Cato’s argument really is, because the US already has a crime problem, it shouldn’t care about enforcing a procedure that reduces crime. If a house is on fire, don’t hose it—light a second one. That is how Cato thinks. Second, because most crime is committed by repeat offenders, you cannot compare the citizen crime rate to the illegal immigrant crime rate directly: Because illegal immigrants are generally deported after they serve their sentences. If we could exile US nationals after they have served their sentences, the crime rate for US nationals would be much lower too.
Because we send illegal immigrants back to their home country after arrest, the immigrant pool of offenders has been purged of recidivists. This makes any direct comparison difficult. Of course, you could look at just first time arrests among US nationals, removing previously arrested from both the denominator and the numerator, but that would be unduly favorable to US citizens as there are likely many people with criminal records in Mexico among the illegal immigrant population. The statistical measurement problem is not easy. [For those of you who are statistically minded, the rest of you can ignore this remark, consider this analogy: statistically speaking, we are comparing a sampling with replacement and a sampling without replacing statistic.]
Another important point is that because they lack ties to the community, it is also harder to catch illegal immigrants who commits crimes: A lot of criminal investigation involves talking to the citizenry and "getting people to narc." If you lack ties to the community, fewer people will recognize you, fewer people will "notice you had a brand new car" when you steal one, etc. In fact, you will even be harder to locate: The police are less likely to have an address on file for you. Arrest statistics are not crime statistics. They are solved crime statistics (more or less; of course, police make mistakes, and not everyone arrested is guilty, I understand). Some portion may have even returned to Mexico---and authorities may not think it worth embarking on a long a complicated extradition process if the crime is insufficiently serious to justify the expense. Cato makes the fundamental error of confusing crime rates with conviction rates.
One final point, you contribute to crime in two ways: The crimes you commit and the crimes your children commit. If you move to areas with gang activity and your children join gangs as a result, that will increase crime too. Of course, I get how pointing this out may seem unfair, but it---in fact---is a factor to consider when modeling illegal immigration's effect on crime.
The real effect of illegal immigration on crime is not simple to measure. But Cato is happy to trick you into thinking it is. The people there are not stupid, so I have to ask myself: Is this simple confirmation bias or overt dishonesty?
There are different kinds of "citizens", of course, people of one kind being ten times as street-crimey as border-crossers and people of another kind being a tenth as street-crimey as border-crossers, with people of other kinds being distributed along the spectrum in between. And only people of a very small number of kinds are capable of committing office-crimes.