(CNN) -

A new survey about preferences and trends in Mexico concludes that one out of every three Mexicans would migrate to the United States if given the opportunity. The survey published Tuesday by the Washington-based Pew Research Center also says that of the 34% of Mexicans who indicated they would like to move to the U.S., 17% "would do so without authorization," meaning without legal documents.

Katie Simmons, senior researcher at the Pew Research Center, says that attitude has changed little in the past five years.

"It's been relatively constant," Simmons said. "We first asked people about this in 2009, and the percentage was 33%, compared to 34% this year."

On the other hand, the survey found that fewer Mexicans have friends or family in the United States. According to Simmons, this means the migration of Mexicans to the United States has continued to decline in the last few years. The number of Mexicans who report having a friend or family member living in the U.S. has fallen to 32%, compared with 42% in 2007.

"The most interesting finding that we reported in terms of migration is this change in the percentage of Mexicans who have friends or relatives in the United States. This percentage is a reflection of the change in net migration. It's an objective indicator of current migration trends," Simmons said.

The Pew Research Center reported in 2012 that net migration from Mexico to the United States fell to zero (and perhaps less) between 2005 and 2010, meaning the number of Mexicans migrating north is equal to or less than those going back to their country.

The latest Pew survey "is based on face-to-face interviews conducted among a representative sample of 1,000 randomly selected adults from across the country between April 21 and May 2, 2014."

The survey covered a wide range of topics including the popularity of current President Enrique Pena Nieto (51%), which declined 6 percentage points in the past year as he pushed through energy and communications reforms some view with suspicion.

Crime continues to be the top concern for Mexicans (79%), followed by corruption of political leaders (72%) and drug cartel-related violence (72%).

The survey also shows that Mexicans seem to have a very positive image of the military (75%), although many people are concerned about human rights violations as the armed forces continue to fight criminal organizations.

The survey has a margin of error of plus or minus 4 percentage points.