The purpose of this paper is to apply recent advances in the econometrics of panel data to a problem that has a clear spatial dimension. We model the dynamic adjustment of real house prices using data at the level of US States. In the last decade, in most OECD countries there has been a significant rise in real house prices. This attracted the attention of many international organisations and central banks. In this paper we consider interactions between housing markets by examining the extent to which real house prices at the State level are driven by fundamentals such as real income, as well as by common shocks, and determine the speed of adjustment of house prices to macroeconomic and local disturbances. We take explicit account of both cross sectional dependence and heterogeneity. This allows us to find a cointegrating relationship between house prices and incomes and to identify a small role for real interest rates. Using this model we then examine the role of spatial factors, in particular the effect of contiguous states by use of a weighting matrix. We are able to identify a significant spatial effect, even after controlling for State specific real incomes, and allowing for a number of unobserved common factors.