It’s both true that the quantity housing construction has declined sharply and also that the unemployment rate has risen sharply, but as Scott Sumner points out for all that people want to keep talking about construction workers you just can’t make the numbers add up on this:
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%
In a well-managed sectoral shock, what happens is a lot of construction workers lose their jobs and then . . . most of them get new jobs. But when you let aggregate demand collapse, that’s not what happens and instead you end up with 10 percent unemployment. Instead of the construction workers getting new jobs, folks who sell things to construction workers lose their jobs and the cascade tumbles forward.