Three years into an economic recovery, falling household incomes and rising poverty rates have leveled off, suggesting the deep slide caused by the recession has finally bottomed out, new census statistics released Tuesday show.

In 2012, median household income nationwide remained at a little more than $51,000, the same as 2011 and ending a four-year downward trend, according to the Current Population Survey. That represents an 8 percent drop from 2007, when the recession officially began.

Last year, 46.5 million people, or 15 percent of the population, lived in poverty, the same as in 2011. That is 2.5 percent higher than pre-recession levels, and as high as it was in the mid-1960s when the War on Poverty was launched.

The poverty and income figures from the census portray a nation still struggling to gain its footing after the recession that officially ended in 2009. Only the most affluent American households are approaching a return to their pre-recession income levels.

The report also shows how incomes have changed little during the span of four decades. That is particularly true for men working full-time, a group whose median income in 2012 was $49,000 — barely higher than their median income of $47,000 in inflation-adjusted dollars in 1970. In the same time frame, median incomes for working women rose from $28,000 to $38,000.

Much of the census report was equally bleak. One in five children, most of them belonging to single-parent households, live in poverty. African Americans experienced the highest poverty rate, 27 percent, with Hispanics close behind, at a little less than 26 percent. That compared with 12 percent for Asians and less than 10 percent for non-Hispanic whites.

Several demographers, economists and sociologists expressed disappointment that income and poverty rates are so stagnant.

“We’re supposed to be in recovery,” said Austin Nichols, a researcher at the Urban Institute. “Poverty rates should be falling because long-term unemployment is falling. And they're not.”

Sheldon Danziger, president of the Russell Sage Foundation and the author of several books on poverty, blamed government policies for the persistently high poverty level — the federal sequestration, the end of extended unemployment insurance benefits and state government layoffs of teachers and firefighters.

“We’re now four years into a slow recovery,” he said. “Government has been making it worse through fiscal austerity. If the economy continues to grow like this, in four or five years the unemployment rate will be back to 5 percent. The poverty rate might fall from 15 percent to 13 percent. And the median earnings of workers might rise by 4 or 5 percent. And, gee, in 2018, America will be back to where it was in 2006. Is that the future that we want?”

Bill Frey, a demographer with the Brookings Institution, said that children in the fast-growing Hispanic community have been particularly vulnerable, accounting for a disproportionate share of the growth in children who have been thrown into poverty since the recession.

“It has to do with people at the lower end of the ladder being the last to be affected by recovery,” he said. “This is a very, very slow trickle down.”

The census report buttresses several recent studies showing an uneven recovery from the recession.

In a report issued this month, Emmanuel Saez, an economist at University of California at Berkeley, said that since the recession ended, family incomes in the top 1 percent grew by 31 percent while everybody else’s incomes rose by just 0.4 percent. Saez said the top 10 percent of households reaped more than half of all income in the nation, the highest percentage since 1917.

If there was one bright spot in the census statistics, it was that about 400,000 more children had health insurance last year than in the previous year.

Caroline Fichtenberg, director of research for the Children’s Defense Fund, said that was largely because of the success of the Children’s Health Insurance Program, which provides health coverage to children from families with incomes too high to qualify for Medicaid coverage.

The census report said 3 million more people had health insurance in 2012, with the increase coming mostly from people with government health insurance, particularly Medicare.

Eight in 10 Americans have health coverage, and more than half get it under employer-provided plans. But company-paid plans have been declining for more than a decade, and the census showed a small decline again in 2012.

Gary Burtless, an economist with the Brookings Institution, said that is largely because insurance companies cannot drop adult children from their parents’ plans until they turn 26. The long-term drop in employer insurance will probably continue, he said.

“They may withdraw offering health insurance to some employees they previously offered it to, reasoning they can get less expensive insurance through a health insurance exchange,” he said. “Even compassionate employers are going to recognize this.”