What was more important in holding the economy close to potential output, residential construction itself, or the housing price bubble? I tend to believe the price-driven balance sheet effects were driving dynamics over this past business cycle.
I still think that the best charts demonstrating this are Timothy Taylor's. The point that housing construction per se is too small to account for the swing in GDP growth is well taken.
The way I would tell the story is that the causal factor was the loosening of mortgage credit standards. Lenders found ways to enable borrowers to take cash out of their homes, through home equity loans and cash-out refinances. Moreover, they found ways to enable borrowers to obtain homes with little or no down payments in the first place. This credit expansion fueled a bubble in housing prices, which in turn allowed more lending against this (artificially-inflated) home equity.
The way I see it, the principal culprit is mortgage lending standards, not monetary policy. As I argued in Not What They Had in Mind, the loosening of mortgage lending standards was encouraged by various regulatory policies that reduced the capital requirements for banks holding mortgage-backed securities. Thus, the balance sheet boom was created by regulatory policy.
The macroeconomic effects of balance-sheet phenomena can be told in either Keynesian or PSST terms. In Keynesian terms, aggregate demand goes up because of debt-fueled consumption and then goes down when the stimulus is withdrawn. The answer is to find another stimulus drug to inject into the economic system.
In PSST terms, the balance-sheet bubble created unsustainable patterns of trade. Businesses built up supply chains to deliver goods and services to people who were living beyond their means, and now those patterns of trade have to change. However, unlike the Keynesian story, there is no simple remedy. Patterns of sustainable specialization and trade have to emerge organically, instead of being artificially created by government living beyond its means.
In the Keynesian model, borrowing money to maintain high public-worker salaries will create trickle-down prosperity for the private sector. In the PSST model, it won't.