Some blockbuster housing numbers released Wednesday mean it is finally time to start grappling with a happy possibility: What would a housing recovery look like in this economy, anyway?

The Census Bureau said that housing starts rose a remarkable 15 percent in September, to their highest rate since July 2008. Analysts had forecast a 2.7 percent gain. The number of housing permits also rose at a double-digit rate, 11.6 percent, compared with the 1.1 percent forecasters were predicting.

For months, a wide range of indicators of the state of the housing market have been pointing to improvement, with evidence that prices, sales and construction activity are all starting to rise after five lean years. It is still anybody’s guess how long the upswing will last and whether the worst is truly over for housing. But Wednesday’s numbers are the most solid evidence yet that the improvement is for real.

First, it helps to understand how deep, and sustained, this housing depression has been. Residential investment — essentially, housing construction and sales activity — has been below 3 percent of gross domestic product every quarter since the fourth quarter of 2008, closing in on four years.

Before this downturn, it had never fallen below 3 percent for even a single quarter (the data go back to 1947).

Housing starts jumped 15 percent in September.

Even in the deep and traumatic 1981 recession, home building never experienced a single quarter as bad as those that have been seen continuously for the past four years.

Part of those dire results are surely attributable to correcting the excesses of the housing bubble, roughly from 2002 through 2007. (As measured by residential investment, the housing boom peaked in the third quarter of 2005, and building activity had fallen to roughly normal levels by the summer of 2007. It was in 2008 that it fell precipitously.)

Here’s the thing, however: The overbuilding of houses during the boom years, while real, was not extraordinary by historical standards. The underbuilding of houses has been far greater than the excess housing construction during the boom relative to demographic trends.

That means that other factors are probably major culprits in the housing weakness of the past four years: A terrible job market that has made people unwilling or unable to get a mortgage, an overhang of foreclosures that has kept the market for houses from clearing and extreme caution by banks and other lenders that has made it hard to get mortgages.

Now each of those trends seems to be healing. Few would argue that a return to the housing bubble days of 2005 is attractive, but what if, over the coming year, housing returned to its longer-term trend?

In the second quarter of 2012, residential investment was 2.39 percent of GDP. As a rough estimate of the longer-term trend for that number, let us use its average level for the entire decade of the 1990s: 4.07 percent. (Using the 1990s is a bit arbitrary; even using various other base lines yields similar numbers.)

If residential investment converged to that longer-term average, it would add 1.7 percentage points to overall growth in the coming year.

In the first six months of 2012, the growth rate of the economy, excluding gains in housing, was about 1.35 percent. If everything else — consumer spending, business investment, exports and government spending — continued growing at the same pace it has in 2012, the gain in housing then would put overall growth in the coming year at about 3.25 percent.

That may not be the kind of gaudy 6 or 7 percent growth witnessed in the aftermath of the 1981 recession, but it would be enough to finally put people back to work in a meaningful way.

And it would be a big improvement from the three years of sluggish, halting growth that have been seen since the current recovery technically began in summer 2009.

That would mean an additional $262 billion in economic activity, which, if recent relationships between dollars of residential investment and housing starts hold up, would translate into an additional 517,000 homes being built every year — meaning that the 872,000 annual rate of housing starts that the Census reported Wednesday would rise by a cumulative 59 percent in the coming 12 months.

While all this may seem like an naively sunny scenario — and it would be great news for the economy if it materializes — keep in mind that it is hardly presenting an outlandish sort of boom for housing.

Rather, this is what would happen if housing returns to its average role in the economy of the pre-bubble 1990s and did so in the coming 12 months.

The dark clouds are these: We don’t know for sure whether the gains in September housing activity are a short-term blip, one of the kinds of ups and downs we have seen too often in this recovery, or something more. And this scenario assumes that the other sectors of the economy keep holding up their current growth rates.

But signs show that some of those sectors, particularly exports and business investment, are losing steam.

If those trends continue, it is all the more important that housing starts to carry its weight and that September turns out to be the beginning of something big.