Housing Supply Elasticity: Proxy for Exogenous House Price Movements Mian and Sufi (2014) say


  We use individual and zip code level data, and exploit cross-sectional variation in house price growth to estimate the impact of rising home values on borrowing and spending. We use the Saiz (2010) housing supply elasticity of a CBSA as an instrument for house price growth, and focus on the heterogeneous effects of house price gains on borrowing and spending.


And, later


  The question we seek to answer is: Are housing wealth shocks also shocks to cash on hand? We answer this question by empirically estimating how changes in housing wealth affect
  household borrowing and spending decisions.


I miss the step on how to get housing wealth shocks as opposed to general equilibrium changes in housing prices. In general, changes in housing wealth are not necessarily exogenous and unanticipated. How does the housing elasticity help to extrapolate exogenous price movements in the housing sector?
The idea is that all else equal, areas with inelastic housing supply (e.g., areas that are surrounded by water, so you can't just build some more houses "over that way") will see greater house price growth, which increases household wealth, and that these differences in supply elasticity are exogenous and uncorrelated with other things that matter. In Saiz (2010), he uses terrain and water data to determine the degree to which the housing supply in different metropolitan areas is constrained by geographic features.

It's a method that really only works (to the extent that it does) when house prices are rising, which would induce housing construction. If house prices are falling, supply elasticity tends to be pretty low— we don't tend to bulldoze homes at a particularly high rate.

With respect to the degree to which house price changes are anticipated, I think the best work on expectations is that done by Case and Shiller over the years, most recently Case, Shiller, and Thompson (2012).