More than three years after the recovery began — in name, at least — the economy is still in a giant hole. But what, precisely, is still dragging it down? What sectors are the culprits? A simple model delivers some answers.

We can start by looking at the difference between what the U.S. economy is capable of producing and what it is actually producing, known as the output gap.

If almost all of the workers who wanted a job had one, factories were working at full speed and office buildings were full, economic activity would be $973 billion higher (at an annual rate) than it actually was in the third quarter.

That is the value of what we are not producing every year because so many factories are idle and so many would-be workers are on the jobless rolls. To see what parts of the economy are responsible for that lost activity, we can look at what proportion of gross domestic product each sector is historically responsible for and gauge their performance in 2012 compared with what would be expected in a world of full employment. (I used the average from 1985 to 2005, but these numbers are fairly stable, so the exact years used doesn’t make much difference.) The result is a simple model that tells us what sectors are underperforming and by how much.

The biggest single sector responsible for the weak economy won’t surprise anyone. Residential investment is a startling 49 percent below what would be expected historically, accounting for $370 billion in “missing” economic activity. This is what one would expect given that housing was a major trigger for the economic crisis. Yet that offers some hope — if housing just returns to its normal role in the economy, 38 percent of the output gap would disappear.

The next-biggest drag on the economy also makes sense. Spending on durable goods — think automobiles, furniture and large appliances — is 18 percent below what it would be in a healthy economy, accounting for $267 billion of the output gap. Americans are still dealing with debt and tighter credit; it is harder to get a car loan, for example, and people are more cautious about big-ticket spending because they are fearful about job prospects and paying down debts racked up in years past. The hole in spending on nondurable goods is substantial as well, at $127 billion. Consumers are holding onto their wallets — a continuing burden for the weak economy.

That said, data out Monday suggest that trends are pointing in the right direction for consumer spending. Personal consumption expenditures rose 0.8 percent in September, the Commerce Department said, as personal income rose 0.4 percent.

The third major contributor to sluggish growth is the pullback in business investment. Corporate America is spending 13 percent less on equipment and software than it would in a healthy economy, accounting for $174 billion in missing economic activity. Less investment in structures — think office buildings, factories and stores — accounts for an additional $69 billion loss. One of the most worrisome signs in Friday’s GDP report was that business spending on equipment and software, which had been improving for the past two years, stopped growing in the third quarter. That, combined with recent data on factory orders, means there’s a risk that this part of the economic gap is poised to widen.

There are other drags on growth, but the big three — housing, consumption and business investment — are the largest culprits.

Trade has been hampering the economy more than history would suggest, but its overall role masks an interesting story. Exports are much higher than historical numbers would suggest, overshooting what our model predicted by $551 billion. But imports, which subtract from GDP, overshoot the model even more, by $670 billion.

Those increases can be partly explained by the growing role of trade in economic activity. But they also reflect the steep run-up in prices for commodities since 2005: The prices of the oil that the United States imports and the agricultural and mined products that it exports have risen.

State and local government spending has been falling over the past three years, taking a toll on the job market. But that drop is not a major hindrance. State and local government spending is only 4.7 percent below where it would be expected in a healthy economy, accounting for $92 billion in lost activity, or about 9 percent of the output gap.

Federal nondefense spending is actually 7 percent above the level that would be expected, contributing an extra $28 billion to economic activity. National defense spending, however, is down 6 percent against forecasts, meaning that overall federal spending is widening the output gap by $28 billion.

There is only one major sector that is outperforming what our model predicts. Although spending on physical goods is well below the forecast, spending on services is 4 percent above what might be expected, contributing an extra $290 billion to the economy.

Part of this is likely due to longer-term shifts in consumer economic behavior, such as eating more restaurant meals and buying fewer groceries. Also, many service sector expenditures can’t be postponed the way the purchase of an automobile can. And many big-ticket services, namely health care and education, have become steadily more expensive relative to cars, computers and other physical goods, and therefore take up a bigger portion of Americans’ spending.

Despite our weak economy, an understanding of the nation’s output gap offers reasons for hope. Housing and personal consumption seem to be recovering more quickly, and if that trend continues, most of the nation’s economic problem will be solved.