Poverty statistics can be used to prove almost anything.

When the Census Bureau reported last week that 46 million Americans, or 15 percent of the population, live in poverty, conservatives said that five decades of the welfare state have had virtually no effect. Liberals answered that laissez-faire economics have kept poverty rates stubbornly high.

This debate is based on a false premise: Poverty isn't as high as the U.S. government says it is. The reason is that federal programs, supported by Democrats and Republicans alike, have dramatically reduced poverty and, by extension, income inequality.

To understand why, let's look at what the numbers don't show. The Census Bureau doesn't count safety-net benefits, including food stamps, housing aid, school lunches and other noncash transfers. Adding the cash value of food stamps alone would lower the poverty population by 3.9 million people. Census data also overcompensate for inflation by ignoring discount prices at big-box outlets such as Wal-Mart Stores, where many low-income families shop. The figures don't even factor in Medicare and Medicaid benefits.

But tax credits are the most overlooked numbers of all. One, the Earned Income Tax Credit, is refundable, meaning that some low-income breadwinners get a check from the Internal Revenue Service even if their earnings are so small that they owe no income tax. Counting that tax credit would decrease the number of people living in poverty by another 5.7 million.

The Census Bureau defines a family of four with income less than $23,021 as impoverished. But a better portrait of poverty in America would count all government benefits and tax credits, raising many households' income considerably. An even truer picture of deprivation would measure consumption (how much a household spends on rent, autos, food and other items) rather than income (how much a household admits to bringing home in earnings). Incomes are unreliable because people are reluctant to reveal how much they make. They are less reticent when asked if they have television sets, cars and air conditioning, or if they eat out and go to movies.

When adjusted for these flaws, the level of poverty is much lower, says a new paper by economists Bruce D. Meyer at the University of Chicago and James X. Sullivan at the University of Notre Dame. Instead of 15 percent, it is only 4 percent to 5 percent. And instead of being higher than it was in 1980, poverty has declined by two-thirds.

In other words, the war on poverty hasn't been won, but it's making inroads. The lion's share of the credit, the professors conclude, goes to the Earned Income Tax Credit, the Child Tax Credit and Social Security.

This may not jibe with Republican presidential nominee Mitt Romney's quip about the "culture of dependency," a trait he ascribed to a remarkable 47 percent of voters. The opposite is true: Antipoverty programs have reduced dependency and encouraged work -- and can be fashioned to work even better.

One option is to strengthen the Earned Income Tax Credit. It began under one Republican president (Gerald Ford), was improved by another (Ronald Reagan), and was made refundable by a Democrat (Bill Clinton) -- in each case with the support of congressional Republicans. Studies show the tax credit was the most important factor in reducing welfare rolls, even more so than the 1996 welfare-reform law. Now geared toward single-parent families, the credit could be expanded to help two-parent families and parents without custody of their children.

Automatic stabilizers are also important and shouldn't be undermined, as the budget blueprint by Rep. Paul Ryan, Romney's running mate, would do. As Bloomberg View columnist Peter Orszag has written, eligibility for food stamps, unemployment insurance and relief to state governments should expand automatically, without waiting for Congress to act, when the economy is weak.

The implications of all this go beyond politics. Poverty statistics are one of the nation's most closely watched indicators of economic well-being. They can help tell us if poverty- fighting programs are working, or if our taxes are being wasted. They can also steer policysetters toward more productive solutions and away from popular yet misguided ideas.

If poverty figures are overstated, for example, then so is income inequality. The most-cited studies don't count government benefits or employer-provided health insurance. There is little doubt that the chasm between the top 1 percent and the 99 percenters is narrower than we have been led to believe. That shouldn't depress liberals or cheer conservatives: The inequality gap is closing because of government programs, not the stagnant incomes of the private sector.