The BLS doesn't claim housing prices fell 7.7% since mid-2006, they claim they rose by 7.7%. Just a minor 39.3% discrepancy with C-S.
BLS is the Bureau of Labor Statistics, the custodians of the official Consumer Price Index. C-S is Case-Shiller, the name for a popular index of house prices. The latter fell by 31.6 percent over the relevant time period. These are cumulative figures, not annual rates of change.
If you are a consumer, you can say that the housing component of your cost of living went up. If you are a renter, rents have gone up. If you are an owner, the decline in the value of your home can be imputed as a "rent" that you paid to live in your house.
If you are in the supply chain in home building, as a builder or a supplier of building materials, then you care about the price of your output. You don't include changes in the price of land tracking changes in the price of your output. If you go to the National Association of Homebuilders, it looks as though framing lumber prices peaked just above $400 in the fall of 2005, hit a trough of just under $200 in the spring of 2009, recovered to around $350 in the spring of 2010, and have dropped back to around $250 more recently. Perhaps that is representative of how the sector's prices have behaved.
If you like Commerce Department numbers, then this table of construction prices might be your choice. It says that prices were about flat in 2007, down 5.2 percent in 2008, down another 4.4 percent in 2009, and were about flat again in 2010.
If you are trying to trace a path from employment to nominal GDP, then you take
total hours worked x output per hour x price of output = nominal GDP.
In terms of growth arithmetic,
growth in total hours worked plus growth in output per hour plus inflation = growth in nominal GDP.
Assuming that total hours worked and nominal GDP are measured correctly, then if you think inflation has been lower than the government statistics show, then output per hour has been higher than those statistics show. Scott's point is that this would mean, in turn, that real wages have increased more than the statistics show. But by the same token, it means that productivity has increased more, and that seems like a wash if you are trying to describe a movement along the aggregate supply curve.