How did two men, whose work is widely respected, reach such different conclusions from data about the same economy? As I read their papers, I realized that they simply asked different questions. Hubbard was fascinated by analyzing the ways in which government intervention can distort otherwise efficient markets; many of Summers’s papers explored the reasons markets aren’t always perfectly efficient.

So one morning this spring, I met Summers and Hubbard in a small, well-appointed room at the Council on Foreign Relations on Manhattan’s Upper East Side to hear them battle it out as if they were preparing to brief the president and leaders of Congress on what must be done to fix our economy right now — what, in other words, is our best 3-point shot. I wanted to hear their answers, of course, but I was also interested in how they made them. I wanted to understand the extent to which empirical economic research can provide objective guidance for policy — and at what point even brilliant, highly trained economists resort to articles of faith.

As we settled in that morning, Hubbard quickly zeroed in on the issue that has defined his career. In regard to the size of the government, Hubbard said the real challenge is the steady rise in so-called entitlement spending. Going forward, he said, government debt will rise partly on account of the increase in the cost of Social Security, Medicare and Medicaid. Already these programs take up around half of all U.S. government spending. As the population ages and as health care costs rise far faster than inflation, these programs could double in cost by 2040. Hubbard goes into great, semi-apocalyptic detail about the effects of taxes and debt in his forthcoming book, “Balance.” It’s a mode he slips into rather easily in person too. Hubbard, usually regarded as a centrist Republican, suddenly started to sound like a member of the Tea Party. “Entitlement programs are on autopilot,” he said. “I’m alarmed. We’re close to the danger zone.”

Then he presented his solution. “I see no reason we need programs that are exactly the same for all Americans,” he said. Hubbard suggested turning Social Security and Medicare into smaller programs that help “the least well off among us.” With smaller social-insurance programs, the government can prevent tax increases and shrink the debt burden. That, he said, would lead to broad economic growth. As he spoke, I began seeing the arc in my mind: a young boy grows up in Central Florida reading Hayek, charts Social Security’s distortions in graduate school and eventually argues to overturn the system. Hubbard would go on to become the architect of George W. Bush’s famous tax cuts, which slashed taxation on dividends and capital gains. His views all seemed to coalesce around a fairly simple idea: the U.S. economy is better off when the government gets out of the way. Cutting the entitle­ment programs was an extension of this. It could free up more capital to further enable virtually everyone to contribute to the economy.

Summers’s worldview seemed to take into account more moving pieces. “It would surely be better to address long-run fiscal issues sooner rather than later,” he said. “But this needs to be done in a balanced way. The highest priority is getting the economy growing.” Summers said that he expected the government debt to grow, because the cost of services that the government pays for — like education and health care — are rising far faster than many of those bought in the private sector. He considered this a problem but a separate one that needed addressing on its own. “We have an enormous amount of work to do as a society to figure out how to contain health care costs,” he said.

As he slid comfortably into the professorial mode I glimpsed a few weeks earlier at Harvard, Summers started to take on Hubbard’s argument directly. He had told me that if tax rates were so dominant in determining economic health, “it wouldn’t be the case that the economy grew fastest when top tax rates were highest.” After all, the U.S. economy did grow quite quickly in the 1950s and 1960s when top tax rates were far higher (income tax was once as high as 91 percent). Lowering taxes on the rich and cutting benefits to the middle class, he said, could also have the opposite of Hubbard’s intended effect. Ambitious middle-class people might see no point in taking risks, fearing that the fix was in and that only the rich could get richer. At some point, Summers became emotional in his defense. He told me that Social Security and Medicare were among the best things about America. They took the group of people that were most vulnerable in our society — the elderly — and made them secure. “Why would you want to get rid of that?” Summers asked rhetorically.

As they continued to trade arguments, seeking to undercut each other, Summers and Hubbard remained calm. Neither raised his voice or interrupted. Hubbard, leaning forward, smiling, began responses with “I want to agree with Larry on . . .” before explaining his many, many disagreements.