A gamma generalised linear model as an alternative to log linear real estate price functions

Abstract

Orientation: Residential property markets play an important role in economies, informing policy development and decision-making. However, measuring quality-adjusted growth is difficult because of the heterogeneity of properties. Hedonic regression is frequently used in real estate econometric studies as a quality-adjusted technique to estimate residential property prices for the development of price indices. Log linear models are typically used to derive these hedonic price functions.

Research purpose: This article develops hedonic pricing functions using generalised linear models for South African residential property listings over a 5-year period.

Motivation for the study: A parametric alternative to the log linear model is investigated to address the limited studies conducted in South Africa. An important feature of this study is the inclusion of different property types and the geographic scope.

Research approach/design and method: The data set consisted of 415 200 residential properties from all over South Africa. The data spanned a period from January 2013 to August 2017. Several generalised linear models were developed and compared.

Main findings: The gamma generalised linear model provided the best overall fit, generalising well to the unseen validation data. An added benefit of this model is that the estimates were kept on the original scale, avoiding the need for back transformation which is an appealing feature of any model. A dummy locational variable was shown to account for the spatial dependency in the data.

Practical/managerial implications: This framework provides property market participants with the ability to quantify the utility derived over the marginal distribution of the physical characteristics of properties. This research presents the groundwork to create a property price index where index number theory could be applied to the counterfactual predicted values obtained from hedonic price models to measure price inflation over time

Contribution/value-add: This study analysed the South African residential property market based on an online company’s data, purportedly covering the entire market. No real estate hedonic price studies have been identified in South Africa with this level of scope. The gamma generalised linear model is a novel candidate to develop parametric real estate hedonic price functions.