Modelling Housing Using Multi-dimensional Panel Data

This chapter surveys housing models using multi-dimensional panels. While there is a vast literature on housing models using two-dimensional panel data, there are only few papers using multi-dimensional panels. This chapter focuses on housing models, residential mobility and location choice models derived from discrete choice theory utilizing multi-dimensional panels. Examples include nested or hierarchical error components models where a house is located in a street, within a block, within a city, within a county, etc. This chapter introduces some basic concepts of utility functions and discrete choice models used for the hedonic functions and the residential mobility and location choices. Then it surveys some papers on multi-dimensional models of housing hedonic price functions focusing on their estimation methods and their main results. This is followed by a survey of some papers on multi-dimensional models of residential mobility and location choice as well as surveying a few papers on dynamic housing models. It shows that both spatial and temporal dimensions in dynamic systems should be included for hedonic housing models and discrete models of residential location in a multi-dimensional framework. But the inclusion of these multiple dimensions greatly complicates the specification and modeling of such systems. Last, the paper concludes with variational Bayesian approximations which are promising future pathways to potentially overcome many problems in applied modelling of housing and illustrate it using hedonic housing estimation for the city of Paris.