RDP 2006-04: Measuring Housing Price Growth – Using Stratification to Improve Median-based Measures 1. Introduction

Developments in housing prices are of great interest to households, policy-makers and those involved in the housing industry. This has been the case both in Australia and in other countries where house price developments are having significant macroeconomic impacts. However, the construction of aggregate measures of housing prices is not a straightforward exercise, and involves addressing a number of conceptual and practical issues. This paper aims to provide a computationally simple method of addressing some of these issues. While the focus of this paper is on measuring house price growth in Australia, the method outlined in this paper would also be feasible and readily adaptable for data from other countries.

One major problem in measuring housing price growth results from the infrequency of transactions and the heterogeneous nature of the housing stock. To be meaningful, price data should be based on transactions prices rather than valuations. But only a relatively small fraction of the housing stock is transacted in any period: in Australia the average turnover is around 6 per cent per year, or just 1½ per cent per quarter, and in other countries the turnover rate is often significantly lower. Given that the sample of transactions in any period may not be representative of the entire housing stock, changes in simple median or mean price measures may not provide good estimates of the pure price change, as they will also reflect compositional effects. In addition, problems associated with compositional change can be exacerbated by problems of data timeliness if there is a systematic lag between when particular sales are agreed to and when they are recorded in a database of transactions. Hence, early estimates of changes in housing prices may be quite unreliable, making it difficult to distinguish in real time between true movements in the housing market from spurious movements due to compositional effects.

If detailed and timely data on transactions are available, it is possible to use regression-based approaches to deal with the problems discussed above. For example, hedonic price regressions and repeat sales regressions can be used to abstract from compositional effects to derive estimates of pure price changes.^[1] However, many of the housing price series produced internationally do not use such techniques but rely on simple measures such as median or mean sales prices. For example, the Real Estate Institute of Australia, the US National Association of Realtors, the Canadian Real Estate Organisation and the Real Estate Institute of New Zealand (REINZ) all publish house price data which are simple median or mean measures. The reason is presumably that the more advanced techniques require detailed data, are typically subject to revision as data for future periods become available, are less transparent, and require the use of statistical techniques that are not as widely used by organisations such as industry bodies.

We show that compositional change can have major impacts on estimates of price changes that are based on simple median measures. Accordingly, we outline and test a simple method for calculating changes in aggregate housing prices that controls for compositional change and which remains robust even when the initial sample of transactions is fairly small. In particular, we propose a method that stratifies individual house sales into different groups so as to minimise the impact of compositional change, and then uses the median prices from those groups to derive an estimate of the overall change in prices. We therefore demonstrate that median prices can be considerably more useful if taken from a stratified data sample compared with a single (unstratified) median taken from the entire data sample.

The particular innovation of the paper is the method of stratification. A standard method of stratification is to divide a city into broad geographical regions. However, changes in regional composition do not necessarily result in problems for median measures; compositional change will only be a significant problem if it results in changes in the proportion of high-and low-priced properties. Accordingly, we group small geographical regions (suburbs) into different strata based on the long-term average price level of houses in those regions, thereby directly addressing the main problem of compositional change. We find that stratifying sales in this manner produces a measure of price growth that is a considerable improvement over an unstratified median; our measure is significantly less noisy than a median and performs better in real time with limited data samples. As the aim of the paper is to look at computationally simple methods of calculating price growth, regression-based techniques are not considered, however, Hansen (2006) provides a complementary analysis using regression techniques. We find that the growth rates produced by our measure line up closely with the more advanced measures contained in Hansen. This leads us to conclude that it is possible to come up with estimates of overall changes in house prices that are very similar to regression-based measures, but are based on simple medians from stratification.

The rest of the paper is organised as follows. In Section 2 we present some data on median house prices and document the strong impact of compositional change. In Section 3, we outline how stratification techniques – a method commonly used in other contexts – can control for compositional change. Section 4 outlines our method of controlling for compositional change, while Section 5 provides an assessment of the resulting measure of housing prices. Section 6 concludes.

Footnote

See Case and Shiller (1987), Meese and Wallace (1997) and Hansen (2006) for further discussion of these methodologies. [1]