In arguing against gun control, Sen. Ted Cruz said that Washington, D.C., and Chicago “for years” have been “right at the top of murder rates,” and claimed that most “jurisdictions with the worst murder rates” have “the very strictest gun control laws.” Cruz distorts the facts:

It’s true that Chicago “has long been at or near the top” in total annual murders, but its murder rate is “nowhere near” the top, according to Pew Research Center’s analysis of FBI data from 1985 through 2012. Chicago’s murder rate in 2014 was 35th highest among cities with 100,000 or more residents, FBI data show.

Washington, D.C., had the highest murder rate eight times during the 28-year period reviewed by Pew. But the last time the District had the highest rate was 1999. In 2014, Washington, D.C., reported 15.9 murders for every 100,000 people — 29th highest in the country.

There is no evidence that gun control laws result in higher murder rates. In fact, studies suggest the opposite: States with a higher number of firearm restrictions have lower firearm deaths. But there is only an association between gun control laws and firearm deaths, not a causal relationship, studies show.

Cruz made his remarks at a town hall event on ABC’s “Good Morning America.” A pastor from Bronx, New York, asked the Texas senator what he would do to stop gun dealers from buying guns in Southern states and “shipping them into my community.”

Cruz, who is running second behind Donald Trump for the Republican presidential nomination, said “the way to solve gun violence, I believe, is targeting the criminals, not targeting law-abiding citizens.”

Cruz, April 18: If you look at the jurisdictions with the worst murder rates, most of them are the ones with the very strictest gun control laws. Because when you put gun control laws in place, the criminals don’t hand over their guns, but the law-abiding citizens do and it ends up leaving them more vulnerable. And so, you look at Washington, D.C. You look at Chicago. Both of them have for years effectively banned firearms and both of them have for years, been right at the top of murder rates.

Let’s start with the murder rates. We looked at Chicago and Washington, D.C., and didn’t find that they are “right at the top of murder rates.”

Murder Rates

Pew Research Center reviewed data for murders that were reported to the FBI from 1985 through 2012 by jurisdictions with populations of 100,000 or more residents. The headline of the Pew article says, “Despite recent shootings, Chicago nowhere near U.S. ‘murder capital.’ ”

“In terms of raw number of murders, Chicago has long been at or near the top of U.S. cities, according to FBI crime statistics,” Pew found. “But Chicago also has some 2.7 million residents, more than any other city except New York and Los Angeles, and you’d expect it to have more murders (and other crimes) than most other cities for that reason alone. Adjust the raw numbers for population size to get a murder rate, and a very different picture emerges.”

Pew Research Center, July 14, 2014: According to the FBI figures, Flint, Mich., had the highest murder rate of any sizeable U.S. city in 2012, the most recent year available. There were 62 murders per 100,000 population (which, coincidentally, was just about Flint’s estimated population that year). Trailing Flint were Detroit (54.6 murders per 100,000), New Orleans (53.2 per 100,000) and Jackson, Miss., (35.8 per 100,000). Chicago, whose population is several times bigger than any of those cities, came in 21st, with 18.5 murders per 100,000 — nearly quadruple the national average, true, but still nowhere near the highest in the country.

So, FBI data show Chicago was not “right at the top of murder rates.” What about Washington, D.C.?

Pew found that Washington, D.C., was one of only six cities that “held the anti-honor of having the nation’s highest murder rate” from 1985 to 2012: “New Orleans (12 times, most recently in 2011); Washington, D.C. (eight times, most recently in 1999); Detroit (four times, most recently 2006), Flint, Mich. (twice, also in 2010); Richmond, Va. (once, in 1997) and Birmingham, Ala. (once, in 2005).”

But as Pew noted, Washington, D.C., hasn’t had the highest murder rate since 1999. A chart on the Pew website shows the District’s rate climbing dramatically in the mid-’80s and into the 1990s before dropping just as dramatically in the last two decades.

The most recent FBI crime statistics available are for 2014. We calculated Chicago’s murder rate at 15.1 murders per 100,000 people, and Washington’s rate at 15.9 per 100,000. St. Louis had the highest murder rate in 2014 with 50 homicides per 100,000 residents — more than three times the rates in Chicago and Washington.

Of the 286 jurisdictions with a population of more than 100,000, Washington, D.C., ranked 29th and Chicago ranked 35th. (See our list of the 50 cities with the highest murder rates in 2014. As we have cautioned before, the FBI data set isn’t ideal because it is voluntary and self-reported.)

We note that the U.S. Supreme Court struck down Chicago’s handgun ban in June 2010 and Washington, D.C.’s handgun ban in 2008. In the year before the court’s rulings, Chicago’s murder rate in 2009 was 16.1. The city with the highest murder rate that year was New Orleans at 51.7 murders for every 100,000 people. In 2007, the year before the court’s ruling on Washington D.C.’s ban, the District had a murder rate of 30.8 in a year when New Orleans had a rate of 94.7 per 100,000.

Gun Laws and Murder Rates

Cruz also said most “jurisdictions with the worst murder rates” have the “very strictest gun control laws,” claiming the restrictions made “law-abiding citizens … more vulnerable” to such violent acts. But there is no evidence that gun control laws result in more murders, and the Cruz campaign did not respond with any evidence when we asked.

David Hemenway, director of the Harvard Injury Control Research Center, told us that “many studies … found that stronger gun laws are associated with lower rates of homicide.” The key word is “associated.” As we have written twice before, researchers have not established a cause-and-effect relationship between stricter gun control laws and less gun violence.

Hemenway, who has written extensively about gun violence, referred us to a study by researchers at Boston Children’s Hospital and the Harvard School of Public Health, including Hemenway, that was published in JAMA Internal Medicine in May 2013. Researchers developed a “legislative strength score,” which ranked states from 0 to 28 based on the strength of their gun control laws, and then “measured the association of the score with state mortality rates” from 2007 to 2010.

The study’s conclusion: “A higher number of firearm laws in a state are associated with a lower rate of firearm fatalities in the state, overall and for suicides and homicides individually. As our study could not determine cause-and-effect relationships, further studies are necessary to define the nature of this association.”

Other studies have reported similar findings.

A study published in January 2014 in the Journal of Trauma and Acute Care Surgery looked specifically at gun laws that were designed to reduce firearm-related injuries among children. Researchers at the University of Arizona divided 44 states into two groups — 11 “strict firearm law states” (SFLs) and 33 “non-strict firearm law states” (non-SFLs) — “based on background checks on firearm sales, permit requirements, assault weapon and large-capacity magazine ban, mandatory child safety lock requirements, and regulations regarding firearms in college and workplaces.” The study then looked at firearm-related injuries of trauma patients 18 years old or younger in those states in 2009.

That study concluded that strict firearm laws “were associated with a lower rate of firearm injuries in children.” Again, researchers found an association but not a causal relationship.

In March, the Lancet published a study that sought to determine “the independent effect of different firearm laws on firearm mortality.” The study, which was done by researchers at Boston University, Columbia University and the University of Bern in Switzerland, looked at 25 state laws. It found that “nine were associated with reduced firearm mortality, nine were associated with increased firearm mortality, and seven had an inconclusive association.”

In general, the report found “state licensing and authorised inspections were associated with lower homicide rates, but record keeping did not reduce homicides.”

Specifically, it found “the three laws most strongly associated with reduced homicide firearm mortality were expansion of background checks for all firearm and ammunition purchases and firearm identification.” However, it also found that child-access prevention laws (CAP) were associated with increased firearm deaths. “[T]he increased risk attributed to firearm locks in our study could be explained by the results of a longitudinal study for which presence of CAP laws was associated with an increased likelihood of unsafe firearm storage in states with fewer firearm policies,” the report said.

All of these findings, again, go to the association between gun laws and firearm deaths. They do not prove a causal relationship between individual laws and firearm deaths — which is what Cruz claimed when citing the murder rates in cities with strict gun control laws.