Application of Copulas to Improve the Modeling of Housing Tenure and Affordability

Abstract

The tenure statuses made by households (renter-occupancy or owner-occupancy) are influenced by a multitude of factors, some of which cannot be directly measured. However, economists are still interested in knowing the relative severity and patterns of influence these factors have on housing tenure status. The purpose of this research was to determine the effect of assuming joint dependency between housing tenure and affordability on the model results. The effect of model-mis-specification on severity and relative importance of the explanatory variables was also assessed. Joint bivariate binary regression was applied to multi-year cross-sectional General Household Survey (GHS) data from Statistics South Africa (STATSA). An assumption of a univariate model when modeling both housing affordability and tenure led to model mis-specification, because most of the coefficients between the univariate and bivariate joint models were significantly different. Model mis-specification also led to significant differences in rankings of the levels of influence of the explanatory variables. Bivariate joint modeling with appropriate error-model copulas improved the model results. Older households that were above 49 years were consistently more likely to be owner-occupiers, and the household head age variable for older households was the most influential factor for housing owner-occupancy and affordability.