Adjusting for Non-Linear Age Effects in the Repeat Sales Index

Abstract

A true constant quality real estate price index should measure the general change in price level free from any change in quality over time. In recent years, the repeat-sales method has been widely used to construct constant quality property price indices. Since buildings depreciate over time, a simple repeat-sales index would under-estimate the growth in property price. The major problem of controlling the effects of age constant in a repeat-sales model arises from the exact multicollinearity between the age variable and the time dummy variables. In this study, we attempt to derive a solution that is theoretically sound but at the same time practical and inexpensive. Our solution is based on the theoretical analysis of varying effects of age on real estate price under different levels of interest rate, which is analogous to the duration analysis of fixed-income instruments. Based on the theoretical analysis, we can disentangle the effects of age from time in the repeat sales model by augmenting the age effects with interest rates. A sample of residential units in Hong Kong sold more than once from Quarter 2 of 1991 to Quarter 1 of 2001 (more than 11,000 repeat sales pairs) are used for the empirical analysis.

Keywords: Age effects, depreciation, duration, multicollinearity, repeat-sales index

JEL Classification: C43, C81, C82, R21, R31