WASHINGTON - To many Americans, the war on poverty declared 50 years ago by President Lyndon Johnson has largely failed. The poverty rate has fallen only to 15 percent from 19 percent in two generations, and 46 million Americans live in households where the government considers their income scarcely adequate.

But looked at a different way, the federal government has succeeded in preventing the poverty rate from climbing far higher. There is broad consensus that the social-welfare programs created since the New Deal have significantly improved living conditions for low-income Americans. At the same time, in recent decades, most of the gains from the private economy have gone to those at the top of the income ladder.

Half a century after Johnson’s now-famed State of the Union address, the debate about the government’s role in creating opportunity and ending deprivation has flared anew, with inequality as acute as it was in the 1920s and the ranks of the poor and near-poor at record highs. Programs such as unemployment insurance and food stamps are keeping millions of families afloat. Republicans have sought to cut both programs, an illustration of the disagreement between the two political parties about the best solutions for lowering the poverty rate as quickly as possible, or eliminating it.

For poverty to decrease, “the low-wage labor market needs to improve,” James Ziliak of the University of Kentucky said. “We need strong economic growth with gains widely distributed. If the private labor market won’t step up to the plate, we’re going to have to strengthen programs to help these people get by and survive.”

In Washington, President Barack Obama has called inequality the “defining challenge of our time.” To that end, he intends to urge states to expand their Medicaid programs to poor, childless adults, and is pushing for an increase in the minimum wage and funding for early-childhood programs.

But conservatives, such as Rep. Paul Ryan of Wisconsin, have looked at the poverty statistics more skeptically, contending that the government has misspent its safety-net money and needs to focus less on support and more on economic and job opportunities.

“The nation should face up to two facts: Poverty rates are too high, especially among children, and spending money on government means-tested programs is at best a partial solution,” Ron Haskins of the Brookings Institution wrote in an assessment of the shortfalls of the war on poverty. Washington already spends enough on anti-poverty programs to lift all Americans out of poverty, he said. “To mount an effective war against poverty,” he added, “we need changes in thepersonal decisions of more young Americans.”

Still, a broad range of researchers interviewed by The New York Times stressed the improvement in the lives of low-income Americans since Johnson started his crusade. Infant mortality has dropped, college completion rates have soared, millions of women have entered the workforce, malnutrition has all but disappeared. After all, when Johnson announced his campaign, parts of Appalachia lacked electricity and indoor plumbing.

Many economists argue that the official poverty rate grossly understates the impact of government programs. The headline poverty rate counts only cash income, not the value of in-kind benefits like food stamps. A fuller accounting suggests that the poverty rate has dropped to 16 percent today, from 26 percent in the late 1960s, economists say.

But high rates of poverty - measured by both the official government yardstick and the alternatives that many economists prefer - have remained a remarkably persistent feature of American society. About 4 in 10 black children live in poverty; for Hispanic children, that figure is about 3 in 10. According to one recent study, as of mid-2011, in any given month 1.7 million households were living on cash income of less than $2 a person a day, with the prevalence of the kind of deep poverty commonly associated with developing nations increasing since the mid-1990s.

Both economic and sociological trends help explain why so many children and adults remain poor, even putting the effects of the recession aside. More parents are raising a child alone, with more infants born out of wedlock. High incarceration rates, especially among black men, keep many families apart. About 30 percent of single mothers live in poverty.

In some cases, government programs have helped fewer families because of program changes and budget cuts, researchers said. For instance, the 1996 Clinton-era welfare overhaul drastically cut the cash assistance available to needy families, often ones headed by single mothers.

“As of 1996, we expected single mothers to go to work,” Ziliak said. “But if they’re shelling out most of their weekly pay in the form of child care, they can’t make sense of doing it.”

The more important driver of the still-high poverty rate, researchers said, is the poor state of the labor market for low-wage workers and spiraling inequality. During the past 30 years, growth has generally failed to translate into income gains for workers - even as the U.S. labor force has become better educated and more skilled.

Above all, the government has proved most successful in aiding the elderly through the New Deal-era Social Security program and the creation of Medicare in the 1960s. The poverty rate among older Americans fell to just 9 percent in 2012 from35 percent in 1959.

But for working-age households, conservatives and liberals agree that government transfer programs alone cannot eliminate poverty. The answer, the White House has said, is in trying to improve households’ earnings before tax and transfer programs take effect.

“Going forward, the biggest potential gains that could be made on poverty would be in raising market incomes,” said Jason Furman, the chairman of Obama’s Council of Economic Advisers. “In the short run, that means things like the minimum wage, and in the long run, things like early education.”

Front Section, Pages 3 on 01/05/2014