This question has significance far beyond either the real estate market or the labor market, because there has been a persistent line of argument from some that the US's current unemployment problem is not the result of insufficient demand, but is instead a "structural" problem resulting from the inability of the US economy to properly match people with available jobs. A frequent explanation for why it suddenly became difficult to match people with jobs in 2008 is that underwater mortgages have locked people in to their houses, reducing labor mobility and making job-matching more difficult.
The evidence presented in this paper indicates that the fall in house prices has indeed caused a "lock-in" effect, but has not significantly impacted labor market efficiency. Here's the abstract:
LOCKED IN THE HOUSE: DO UNDERWATER MORTGAGES REDUCE LABOR MARKET MOBILITY?This is a significant piece of evidence against the "structural unemployment" explanation for the US's high and persistent unemployment rate. Yes, labor market inefficiencies do certainly exist, and there are a variety of reasons why economies don't always perfectly match unemployed people with available jobs. But the underwater mortgage "lock-in" phenomenon that has been cited as the primary reason why the US's labor market suddenly got so much worse starting in 2008 simply does not match the evidence.
The collapse of the housing boom led to an unprecedented number of homeowners who are “underwater”, that is, owe more on their mortgage than their homes are worth. These homeowners cannot move without incurring significant losses on their homes, possibly causing a “lock-in” effect reducing geographic mobility. This raises concerns that a reduction in labor market mobility may hamper the ability to move to accept employment in another geographic market, degrading labor market efficiency and contributing to higher structural unemployment.
This paper examines housing market turnover and finds significant evidence of a lock-in effect. The lock-in, however, results almost entirely from a decline in within-county moves. As local moves are generally within the same geographic job market, this decline is not likely to affect labor market matching. In contrast, moves out-of-state, which are more likely to be in response to new employment opportunities, show no decline, and in fact are higher in counties with greater house price declines. Housing market lock-in does not appear to have degraded the efficiency of the labor market and does not appear to have contributed to a higher unemployment rate.
As a result, if we want to understand why unemployment has been so persistently high in the US since 2008, we have to look beyond "structural" or supply-side explanations. Once again, the far simpler explanation seems to better match the evidence: there's just not enough demand, so businesses aren't hiring, and people remain unemployed.