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This paragraph is the core of Mitt Romney’s case against President Obama:

What do we have to show for three and a half years of President Obama? Is it easier to make ends meet? Is it easier to sell your home or buy a new one? Have you saved what you needed for retirement? Are you making more in your job? Do you have a better chance to get a better job? Do you pay less at the pump?

In other words: Are you better off now than you were three and a half years ago?

This is a good question to ask. But we need to be a bit more sophisticated about it. Three and a half years ago, for instance, Barack Obama wasn’t yet president. The date was Oct. 25, 2008, and Obama hadn’t even won the election yet, much less taken office.

The National Bureau of Economic Research says the recession officially began in December 2007. The worst of it came in the fourth quarter of 2008. Obama was inaugurated on Jan. 20, 2009. The time frame Romney chose, in other words, thrusts the very worst of the recession into Obama’s lap despite the fact that he wasn’t even president yet. It’s like blaming a fireman for the damage the blaze did before he arrived.

But we need some way to judge Obama. One possibility is to simply start the clock the day Obama was inaugurated. That’s not a particularly smart approach, though. Presumably, we want to know the effects of the decisions Obama made. While it’s true that the economy lost a lot of jobs in February 2009, it’s hard to see how you could fairly peg those on Obama. The guy had been president for less than two weeks..

“There are significant lags between the time a president proposes a policy, the time it is enacted by Congress and the time necessary for it to take effect,” says Laura D’Andrea Tyson, who served as President Clinton’s chief economist. “These lags should be taken into account in measuring the economy’s job performance under a president. The first year probably should not count at all in terms of assessing the effects of a new administration’s policies.”

We can argue whether it should be a year or nine months or 16 months, but let’s say a year. The stimulus, for instance, spent most of its money in 2010, not in 2009. So let’s start there: January 2010.

Since January 2010, the economy has, on net, created 3.5 million jobs. Real disposable income has increased by 1.8 percent in 2010, and 1.3 percent in 2011. The net private savings rate is up. Housing prices have continued to fall. Gas prices have risen by about $1.20.

So, to Romney’s list, it is easier to get a job, most workers are making more money, and most people are saving more. But the housing market has remained soft, and gas prices are up. So are we better off? Sure, but we’re not in great shape, either.

It would be nice to stop there. That’s clean. It’s easy. But the unsatisfying truth is that you can’t just draw a graph from the beginning of 2009, or the beginning of 2010, and judge Obama based on whether the line went up or down. Believe me: If you could do that, I would have drawn the graph.

But presidents influence economies. They don’t — with the possible exception of Kim Jong-un — control them. So the question isn’t just what happened after Obama’s policies began to take effect? It’s what could have happened if Obama had made different choices?

Perhaps we would have added even more jobs. Perhaps economic growth would have been slower. Perhaps gas prices would have risen more quickly. Perhaps they would have risen more slowly, but Moammar Gaddafi would still be in power.

That is to say, the question isn’t “are you better off now than you were two years ago?” It’s “are you better off now than you would have been had Mitt Romney been president?” And that, unfortunately, is much more complicated.

I tried to ask a related question — what more could have been done to speed the recovery? — in this article. Unfortunately, Romney’s speech was devoid of any policy content, much less a detailed argument for how the past three years could have been managed differently. Which is somewhat surprising, because one of the wiser things written on the difficulty of evaluating presidential records came from Greg Mankiw, a Harvard economist who advises Romney.

“Randomness is a fact of economic life,” Mankiw wrote on his blog in January 2009, “and it would be a mistake to judge a president by the economic outcome during his administration. It is better to look at the decisions the president made, and to acknowledge that the outcome is a function of those decisions and many other factors not under his control. As an economist, I have views about what best practices are for economic policy, and I judge presidents by how closely they adhere to those principles.”

“Unfortunately,” he added, “that evaluation process is not quite as simple and objective as the reader might have hoped for. But I don’t think there is a better alternative.”