“Deficits exist because politicians are addicted to spending other people’s money,” Brown said in a statement included with his response to the Globe.

Both candidates said they would cut or eliminate agricultural subsidies. They would also reduce defense spending, which in Warren’s case would mean an accelerated exit from Afghanistan, for a savings estimated by the committee at $36 billion. She did not outline a time frame. Brown would stick to the current timeline for withdrawal, and would also cut nonwar defense spending, such as a widely criticized missile system designed to replace the Patriot missile. His cuts are estimated to save $100 billion over 10 years.

Apart from a repeal of President Obama’s health care overhaul, Brown told the Globe he would consolidate federal programs identified as redundant by the Government Accounting Office, such as several food safety and homeland security programs. Warren would let the Bush tax cuts expire for those earning at least $250,000 a year, and raise estate taxes to their 2009 levels. She would also impose the so-called Buffett Rule, which would require those earning more than $1 million to pay a 30 percent effective tax rate.

The nation’s budget deficit has been identified by many voters, analysts, and political leaders as a priority. It has also been the source of significant gridlock in Washington, nearly paralyzing the economy last summer when talks over the debt repeatedly broke down.

The Globe asked three think tanks to review the candidates’ answers. One of them, the Committee for a Responsible Federal Budget Project, a bipartisan group, provided a detailed fiscal breakdown.

Although the questions posed by the Globe provide a meaningful sample of the candidates’ views on the budget, they do not represent a complete plan. In fact, neither candidate has offered a comprehensive proposal to confront the problem.

Though Brown has made the deficit a larger issue in his campaign, an analysis prepared for the Globe by a nonpartisan group showed that responses offered by Warren, and positions taken on her website, would trim 67 percent more from the debt over 10 years than those offered by Brown.

In response to a request from the Globe, the two competitors in the nation’s most high-profile Senate battle provided five ideas for bridging the nation’s $1.2 trillion deficit, with the results highlighting why the problem has deadlocked Washington. The candidates were also asked to explain what cuts they would make to entitlement programs, and to describe which revenues they would raise.

Democrat Elizabeth Warren would impose higher taxes on top earners, end oil subsidies, and raise estate taxes to cut the federal deficit. Senator Scott Brown would repeal President Obama’s health law, freeze federal pay, and consolidate redundant federal agencies.

Improving the economy will reduce the deficit, he added.

Warren said in her response that “Our first response should be to change the policies that got us here in the first place: end the Bush tax cuts on people earning more than $250,000; end the war in Afghanistan; and take steps to make sure Wall Street can never again bring our economy to its knees.”

Brown has decried spending in Washington and the inability of the two parties to find common ground. He has voted in favor of a balanced budget amendment and the so-called “Cut, Cap, and Balance” bill which would have sliced $111 billion from this year’s budget by imposing deep cuts, and would significantly limit future spending. The analysis does not factor in the Cut, Cap and Balance proposals because the bill did not specify where those cuts would be made. Democrats argue that the bill’s tough provisions would gut entitlement programs.

Brown has also signed the no-new-taxes pledge put forth by activist Grover Norquist, but said on his website that he is “open to raising revenues by closing loopholes as part of comprehensive tax reform so long as it results in lower rates for everyone and doesn’t just grow government.”

Warren has argued for what Democrats characterize as tax fairness, saying that requires the wealthy to pay more. She has also proposed several unspecified additional spending programs, including money for transportation, energy, and education.

The analysis performed by the budget project committee showed that Warren’s ideas would trim $1.029 trillion from the nation’s projected debt and interest over the next decade. Brown’s ideas would reduce the debt and interest by $614.4 billion over the same period, according to the analysis.

The Committee for a Responsible Federal Budget Project was founded in 1981 by two former US House members, Connecticut Democrat Robert Giaimo and Oklahoma Republican Henry Bellmon, and its current board includes prominent deficit hawks from the Reagan and Clinton administrations.

The group estimated that Congress would need to chop at least $4.5 to $5 trillion in deficit spending and interest costs in the next decade to begin stabilizing the national debt in a serious way.

“Neither one of them have proposals in their responses to you that come anywhere near tackling that problem,” said Jeff Vanke, senior policy analyst for the committee, who conducted the analysis.

Robert L. Bixby, executive director of the Concord Coalition, a nonpartisan deficit reduction group, said Brown offered a response that is inadequate in recognizing the need for more revenues and that Warren, who would not entertain any changes to Social Security or Medicare, offered a response that is inadequate in addressing the need for entitlement cuts.