Price of a dwelling consists of the physical structure together with the value of land upon which the house is build. Similarly, the growth rate of the price of a house is the weighted average of increase in the value of the structure and appreciation of land. The price of the structure is typically measured as the replacement cost of the physical building. In empirical analysis the volatility of replacement cost is typically catered for by construction cost index. Land, in turn, is the factor that makes a house worth more than the cost of putting up a new structure of similar size and quality on a vacant lot. In general, urban land prices are expected to be more volatile than the construction costs. In particular, in a growing metropolitan area it is expected that land price level grows faster than the construction costs. Therefore, it is expected that the elasticity of housing prices with respect to the construction costs is time-varying. Nevertheless, the changes in the elasticity and their implications have not been considered rigorously in the previous empirical literature. This study applies smooth transition regression model to allow for time-variation in the elasticity of housing prices with respect to the construction costs and employs quarterly data over 1987-2006 from Helsinki. The analysis gives information about the share of the value of land of the total value of housing in the area. The findings are of significance for the predictability of housing prices and of housing price volatility.