Recently there has been some discussion of housing in the economy that looked at housing starts versus the long term trend of housing starts and concluded that starts have been so far below trend over the last few years that it should offset the excess housing built before the recession.
If the excess housing stock has been worked down the stage would be set for a rebound in housing starts and stronger growth in construction employment.

I have major problems with that analysis that is based on the assumption that trend demand was the same as trend supply. Several variables enter into determining the demand for housing. A couple include income trends and interest rates. While these are important determinants of the short run cyclical trends in housing the factor that drive the long run secular housing demand is household formation. Moreover, there is a tendency to assume that household formation has a flat or rising trend because of population growth. But actually, the long run trend for household formation has been down. In the 1970s-80s the baby boomers becoming adults and forming their own household inflated household formations. In more recent years the baby bust after the baby boom and the poor economy has held household formation down as young adults have had to continue to live with their parents. Recently household formation has been roughly half what it was in the the 1970-80s.

If you look at the smoothed data it shows that housing completions is strongly tied to household formations. Basically the data implies that back in the 1970s-80s household formation was strong enough to justify annual housing starts and/or completions of over 2 million. But in recent years that has not been true.

If you regress housing completion against household formation you get an equation that implies that housing starts or completions should be about 1.12 times household formation. This difference stems largely from the demand for second homes and the destruction of old housing stock But note that the average age of the US housing stock is about 29 years and the old homes that are destroyed would on average be much older and stem from an era when housing starts were much lower.

But if you work on the premise that housing demand is equal to 1.12 times household formation rather than just looking at the trend of housing starts you get a very different view of how much excess housing stocks there is. It shows that demand has just recently started to exceed the supply of new homes.

Moreover, if you look at the cumulative difference it shows that the current excess stock of homes has barely peaked and is still about some 700,000 houses. Compared to the low level of housing starts in recent years that implies that the excess stock of homes is roughly equal to the number of houses built in recent years. This implies that it will be a long time before the market works down the excess stock. This is in sharp contrast to the analysis that just compares housing starts to its long term trend.