Metropolitan house prices in South Africa: Do they converge?

The question this paper investigates is whether or not different metropolitan areas each constitute a separate housing market or whether or not there is a single South African housing market. Theory on the Law of One Price suggests that if products or geographic areas belong in the same market, their absolute prices must converge, so that their relative prices are stationary. By using cross-sectional time series data of five metropolitan areas, the paper tests for the Law of One Price by applying the Im, Pesaran and Shin panel unit root test. The paper finds strong evidence of convergence in large middle-segment house prices and weaker support for convergence in medium middle-segment house prices. In addition, the paper finds no evidence for convergence in small middle-segment house prices. This suggests the existence of a national market for large and possibly middle-segment houses in metropolitan areas, but separate metropolitan markets for small middle-segment houses. In addition, the paper estimates the speed of convergence and finds that large middle-segment house prices converge within two to seven quarters, while the speed of convergence for medium middle-segment house prices in three of the five areas is five to eight quarters.