It's often said that undocumented immigrants live "in the shadows," and that's true in at least two ways. Not only must they often hide their identities in order to work, but they are also largely invisible to researchers. Since it's so difficult to identify them in surveys, we know little about how they live, their health, their education, their finances, and their plans for the long term.

A new study on the behavior of children in undocumented families in Los Angeles casts some light into those shadows, with disturbing results. The findings are particularly relevant this week, as a crisis in Congress worsens over President Obama's offer to defer deportation for millions of undocumented parents whose children are citizens or are in the country legally.

The study by researchers at Pennsylvania State University and Hunter College, City University of New York, relied on data from a representative survey of Los Angeles households of all types. The researchers focused on responses for 2,535 children, about 14 percent of whom had an undocumented mother.

Among Mexican immigrant families, those headed by undocumented parents were more likely than those headed by legal immigrants to report that their children were withdrawn, anxious or fearful, or that their children argued, acted out or demanded attention.

Janet Murguía, president and CEO of Washington-based advocacy organization National Council of La Raza, said her group believes they will "prevail" in the debate over immigration reform. (AP)

The undocumented mothers were also more likely not to have completed high school and to be poor and single, and they described their neighborhoods as less safe for children. Yet even focusing on the children of legal immigrants with these same disadvantages, the researchers found that the children of undocumented parents had more frequent behavioral problems.

What's more, undocumented mothers were less likely to be depressed, possibly because depression discourages people from attempting to cross the border illegally. Depression in parents is associated with misbehavior among children, so in this regard, children of undocumented immigrants had an advantage, but not one that compensated for the psychological effect of simply being in the country illegally.

In other words, just having parents who are undocumented is uniquely damaging to a child's well being.

"It's not just the fact of being poor, or just the fact of having parents with fewer resources," said Nancy Landale, one of the authors of the paper and a professor at Penn State. "There's something else about being a child in an undocumented family."

Other research has found that even very young children can be aware of the risks of being separated from their parents, that they feel ashamed of their family's status in the country and that they don't tell their friends at school about where their parents are from.

Of the children with undocumented mothers in the study, 59 percent were U.S. citizens, so the results suggest the effects that immigration policies, past and present, are having on the minds of a huge number of American children.

"Kids often just get left out of the debate, which is why we have some of the immigration policies we have now, which don't really make sense for kids," said Wendy Cervantes of First Focus, an organization that advocates for children and families in federal policymaking. "It’s important to think about the impact for children."

About 4.5 million children nationwide are U.S. citizens with undocumented parents, according to the Pew Research Center. (By way of comparison, there are about 70 million children in the country altogether.) These are worrisome figures, since even among American kids with parents are also citizens, family disadvantages have negative effects that endure as a child grows up and becomes an adult.