Land and building separation based on Shapley values

Abstract

The total value apportionment between land and building components remains an international issue both in theory and in practice. There are several concepts and methods of value separation, each leading to approximate estimations and therefore to divergent opinions about their reliability. In this paper, we present an alternative method of value apportionment based on Shapley’s scheme of values, well recognized in the coalitional game theory. The practicality of this method is verified using observed prices of 14,715 residential properties sold during the year 2019 over all the 27 districts in Montreal (Canada). This unique data comes with detailed information about the essential attributes of the land and the building components. The empirical results of the method presented in this work are in line with practical expectations of total and separate values, either taken case-by-case or in aggregation per district. They are indeed encouraging when compared to the results of two other independent methods (i.e., the city evaluations and the OLS predictions) for the same properties. The results are interesting not only regarding the separation of value but also in several other related aspects. For instance, land values are often close to or even higher than the building values. This shows a phenomenon of building depreciation and land value appreciation. Some districts seem to favor the quality of the building, others being influenced by the location and quality of the land. Interestingly, in contrast to what is believed in practice, a good quality parcel of land does not necessarily have a good quality building according to the results.