Residential Investment vs Construction Payrolls

There's some disagreement out there between those who see the recession as a "reallocation" shock resulting from a change in the composition of output (with the implication that a significant proportion of unemployment is "structural," because workers have the wrong skills and are in the wrong locations), and those who see it as primarily a phenomenon of aggregate demand (AD).  The two stories are not mutually exclusive, but I'm with those who would put more weight on the AD side.  After all, the economy is continually reallocating resources, creating and destroying firms and jobs, and usually manages this without an aggregate downturn; as Brad DeLong puts it:

"Reallocation" occurs when people are pulled out of unemployment or jobs in which their marginal product is low by opportunities in expanding businesses. "Reallocation" does not occur when people lose their jobs and pile up as unemployed. "Reallocation" occurs not in depressions but in booms.

Arguing against the reallocation story, Scott Sumner points out that most of the decline in housing occurred prior to the recession:

Yes, housing output was low in 2009 and unemployment was high.  But is there a causal relationship?  I say no.  Housing starts peaked in January 2006, and then fell steadily for years:
January 2006 — housing starts = 2.303 million, unemployment = 4.7%
April 2008 — housing starts = 1.008 million, unemployment = 4.9%
October 2009 — housing starts = 527,000, unemployment = 10.1%
So housing starts fall by 1.3 million over 27 months, and unemployment hardly changes.  Looks like those construction workers found other jobs...

You can see this in a graph of real residential investment (red), which falls from nearly $800bn to $500bn (in 2005$, at annual rates) from the beginning of 2006 through the end of 2007.  Most of the increase in the unemployment rate (green) occurs later, in 2008 and early 2009.

That seems to suggest that the economy was smoothly managing a significant reallocation of resources out of construction until the end of 2007.  However, while residential investment was falling like a rock in 2006-07, the decline in construction payrolls comes later, and really gets going in 2008-09.

My hunch is that what is going on here is an example of "labor hoarding" - the tendency of firms not to adjust inputs immediately when output changes, because it is costly to do so.  Initially, construction companies may not have been sure whether the decline was temporary or permanent; it may therefore have made sense to keep people on the payroll so that they would be ready to respond if business picked up.

That doesn't validate the reallocation hypothesis, but it is true that there were alot of construction workers among those losing their jobs in 2008 (but there were job losses throughout the economy, not just construction, of course, as an AD decline implies).