Over the past year, everyone has come to agree that a housing recovery is happening. It wasn’t happening everywhere, but overall , the country was seeing a housing revival. But over the past couple of months, this recovery has started to stall and most people haven’t noticed yet.

Look at housing starts:

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Housing starts increased from the end of 2011 through most of 2012, but have since fluctuated between around 850,000/month and 1,000,000/month. In fact, starts are in a downward trajectory the last couple of months. In July, single-family housing starts fell 2.2%, against expectations of growth, to reach their lowest levels since November of last year. The data may be noisy, but the overall trend in 2013 is clear: housing starts have stalled.

So far, it’s not clear that people have noticed. Take Wonkblog’s Neil Irwin, who wrote about housing starts last week. He noted the dual forces of increased housing starts and rising mortgage rates, concluding:

But the July data is the first real evidence we’ve seen of whether higher mortgage rates will affect the housing industry more broadly. And the early signs, at least, are that builders are not being scared off by higher mortgage rates that make the houses they sell less affordable.

The data seems to tell the exact opposite story.

As Irwin notes, interest rates have risen dramatically since May:Since then, housing starts have fluctuated. The increase in July was just the result of a poor result in June. Housing starts are still below there May level. So, as mortgage rates have risen, are builders “not being scared off”? The answer is unclear. It’s certainly, not a “yes,” as Irwin writes. It’s also only a couple of months of data. But it’s worrisome data at that. The economy is already recovering at a tepid place and a slowdown in housing would further reduce it.

This is yet another fundamental reason that President Obama should nominate Janet Yellen to head the Federal Reserve. Yellen is more dovish than Larry Summers and at least one economist believes the recent rise in rates is because Wall Street fears a Summers-led Fed would reduce asset purchases faster than a Yellen-led one would. If Obama does select Summers and interest rates rise, it could lead to even further contraction in the housing market and hamper the recovery even more. Given the recent data, that’s not a risk the President should take.