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Trump has claimed numerous times that part of the reason we need to close the border is that the illegal immigrants are prone to crimes. I want to check these claims. Are illegal immigrants more prone to committing crimes then the average US citizen?

Obviously being an illegal immigrant is a crime itself, but for this question I want to ignore any crimes that are due to their illegal status, such as not paying taxes. I'm more interested in serious crimes, felonies and violent crimes. I'm also interested in rape as the most common accusation made by Trump. Ideally I'd prefer an answer that separately answers the question of whether illegal immigrants are more prone to rape in addition to whether they are more prone to non-rape crimes if possible.

This question refers specifically to illegal immigrants to the United States. I'll accept statistics that look at all illegal immigrants, or that look only at Hispanic illegal immigrants, since Trump often refers to Hispanic illegal Immigrants as if they are the sole form of illegal immigrant.

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    It would help to have a specific claim (whether from Trump or not). – Oddthinking Oct 23 '16 at 14:06
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    Related question: Other countries. Also, a similar poorly worded question was asked before, and it eventually was edited to be very similar to this question, but no consensus was reached on the wording, so it was never re-opened. – Oddthinking Oct 23 '16 at 14:08
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    The exact claim would be important. It's possible for illegals to commit fewer crimes on average per capita but still account for a disproportionate share of the total criminal activity if the population is quite polarized. For example, a large proportion may be keeping their heads down and avoiding risks, while another portion of the group just doesn't care. In which case, either side could quote valid statistics that would appear to support their agenda. – Spehro Pefhany Oct 24 '16 at 11:08
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    There is no real way to tell without looking at a very specific claim. Are we looking at reported crimes, or crimes that are suspected? Are we looking at enditements or convictions, maybe arrests? What about other "paperwork" crimes like false documents? Where is the line on those. Many are civil issues and not "crimes", but tax issues are crimes (sometimes). In order to really look at the claim, it would need to be very specific. usatoday.com/story/news/nation/2015/07/16/… is a good read. – coteyr Oct 24 '16 at 17:45
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    You state that you want to "ignore any crimes that are due to their illegal status, such as not paying taxes," but it may help you narrow the focus of your question to know that in fact illegal immigrants pay millions of dollars of taxes in each state annually, and that this is counter to Trump's claims as well. usnews.com/news/articles/2016-03-01/… – Danica Stone Oct 27 '16 at 18:16
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TL;DR: We don't know. Reported crimes are actually lower, but that may not reflect the real crime rate. There is no evidence that it is higher, only speculation.

Immigrant crime statistics show less crime

There have been quite a few studies on this. One review found

With few exceptions, immigrants are less crime prone than natives or have no effect on crime rates. As described below, the research is fairly one-sided.

There are some issues with the studies. For example, one type of analysis compares incarceration rates. But this isn't a good basis for comparison. The courts have an additional option with illegal immigrants that they do not have with citizens. The courts can deport illegal immigrants--even if not found guilty of a crime. So those people are never incarcerated and wouldn't show up in those statistics.

Illegal immigrants are less likely to report crimes

ThinkProgress reports

A new study released reveals that Latinos are less likely to report crimes to the police because they are afraid of being asked of their immigration status.

Why would this affect crime statistics regarding crimes committed by illegal immigrants? Because people mostly commit crimes against others like themselves. For example, the FBI's Expanded Homicide Data Table 6 shows that each grouping (white, black, Hispanic, etc.) is most likely to commit crimes against its own group. It's unclear how much this reporting discrepancy causes statistics to undercount crimes by illegal immigrants, but this would have a disproportionate impact on illegal immigrants relative to the native born. As a proxy, Hispanics report Hispanic offenders more than three times as often as non-Hispanic offenders: 439 to 123 in the statistics.

We don't have a good study of how much crime is not reported. Like with rape statistics, it is difficult to accurately estimate what is not reported. We can only point out that underreporting has a disproportionate impact on illegal immigrant statistics relative to citizen statistics.

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    I've removed your personal speculation. Please limit your answer to what the evidence shows and to answering the question. – Sklivvz Oct 24 '16 at 8:42
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    The claim is "Trump has claimed numerous times that part of the reason we need to close the border is that the illegal immigrants are prone to crimes." The part you call "personal speculation" is directly responsive to that--which is the actual claim of the poster's question and is in fact what most people want to know. Another way of saying the same thing: if we increase border enforcement, would it decrease crime? Since that is the actual policy under consideration. The answer is that we don't know what would happen in that case. There is some reason to believe that it would. – Brythan Oct 24 '16 at 14:08
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    Thanks for pointing out crime is underreported in immigrant communities; legal, illegal or otherwise. – JakeGould Oct 25 '16 at 1:32
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    @Sklivvz - editing doesn't serve for you to effectively rewrite someone else's answer to what your answer would be. If you think that more than 30% of this answer is crap, downvote, write your own, and move along. This is ridiculous. – Davor Oct 25 '16 at 19:27
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    For people who can't see deleted part it's available here. – Daerdemandt Oct 25 '16 at 21:59
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No.

Numerous studies show that immigrants (legal and undocumented) are actually less likely to commit violent crime.

From The Wall Street Journal piece "The Mythical Connection Between Immigrants and Crime":

Numerous studies going back more than a century have shown that immigrants—regardless of nationality or legal status—are less likely than the native population to commit violent crimes or to be incarcerated.

A report by the American Immigration Council, published in 2015:

For more than a century, innumerable studies have confirmed two simple yet powerful truths about the relationship between immigration and crime: immigrants are less likely to commit serious crimes or be behind bars than the native-born, and high rates of immigration are associated with lower rates of violent crime and property crime.

and

A variety of different studies using different methodologies have found that immigrants are less likely than the native-born to engage in either violent or nonviolent “antisocial” behaviors; that immigrants are less likely than the native-born to be repeat offenders among “high risk” adolescents; and that immigrant youth who were students in U.S. middle and high schools in the mid-1990s and are now young adults have among the lowest delinquency rates of all young people.

and

Despite the abundance of evidence that immigration is not linked to higher crime rates, and that immigrants are less likely to be criminals than the native-born, many U.S. policymakers succumb to their fears and prejudices about what they imagine immigrants to be.

This 2015 Washington Post piece (scroll down through the article) runs up a list of sources that support the claim that there legal and illegal immigrants are less likely to commit violent crime.

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    IMO this answer could be improved by including the actual numbers and hard statistics these statements are based on. Or at least some notable examples of numbers. – Revetahw says Reinstate Monica Oct 23 '16 at 20:47
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    At least some of your quotes are about immigrants as a whole, not illegal ones. – Andrew Grimm Oct 23 '16 at 21:49
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    In your answer you told Numerous studies but provided nothing to back it up. All you have is some NY times article, and report that tells that innumerable studies have confirmed. – Salvador Dali Oct 24 '16 at 6:04
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    @SalvadorDali Exactly. Can you imagine if someone posted an answer here, but the source of such loose statements were Breitbart or Fox News? They would have (quite rightly) been downvoted and asked to provide hard numbers and statistics. Why should we hold the WSJ to a different standard? We know FN and BB are ideologically biased and dishonest, but are we just going to give the WSJ carte blanche? This is inappropriate for a skeptics site. This answer desperately needs hard statistics, and in the absence of that, it's very low quality as per the help center, IMO. – Revetahw says Reinstate Monica Oct 24 '16 at 15:27
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    Rougon: I don't care what political affiliation the WSJ purports to have. I don't care who says what. This is Skeptics and for a question about statistics we need answers that cite hard statistics. I don't know why this is upvoted so highly. You're saying that there are no credible statistics on this. (I think I agree, BTW.) If that's the case, then how exactly did the WSJ come to their conclusions? Do you know? Or did you just take the WSJ at their word? Because that would be the opposite of skepticism, and completely contrary to the help center. CC: @SalvadorDali – Revetahw says Reinstate Monica Oct 24 '16 at 15:44
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One way to know if illegal immigrants commit more crimes would be to examine the number or people who report being victimized and see if it's higher in places where illegal immigrants are more likely to live. Or in other words, to examine whether sanctuary city policies increase the crime rate.

Researchers Daniel Martinez of U of Arizona, Ricardo Martinez-Schuldt of UNC Chapel Hill, and Guillermo Cantor of the American Immigration Council, published their summary of the current science on sanctuary cities (what they call "limited cooperation policies") and crime, which is surprisingly limited: only four studies were available as of November 2017.

The studies that were conducted contradict the scary narratives about violent cop-killing criminals and illegal immigration. The researchers write:

For the most part, it appears that jurisdictions with limited cooperation policies are either safer from crime or no different than jurisdictions without such policies (Wong, 2017; Gonzalez et al., 2017). Furthermore, limited cooperation policies may indirectly reduce crime by magnifying the crime‐reducing effects of immigration (Martínez‐Schuldt & Martínez, n.d.; Lyons et al., 2013; Ousey & Kubrin, 2017).

How can this be? They suggest that "limited cooperation policies" actually improve communication between the folks who live in the US but are undocumented and the local police force and sheriffs, an effect they call a "spiral of trust", which "strengthens formal and informal social control through community organization, thus reducing crime."

The researchers acknowledge that there is a need for better knowledge of the victims who may not report crimes. But not knowing this is no support for the political narrative that illegal immigrants make America unsafe: a citizen concerned about his or her own safety will not be affected.

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