Median Price Indices

Overview

The median price series forms an index of price levels in the residential real estate market by tracking the median price of transacted properties in a given time period. It is relatively straightforward to implement and is inclusive of all sales. It can be calculated for any period and region in which at least one sale has occurred.

However, the median price series is subject to severe “compositional bias.” Compositional bias refers to movements in an index that are the result of changes in the average quality of homes sold in a given period rather than movements in the true underlying index. That is, movements in the median price series may simply reflect the quality (and hence, prices) of houses sold at a point in time, rather than actual price movements in the total housing stock.

Stratification is a technique for creating more homogenous subsets from a highly heterogeneous total population. Additionally, stratified indices are able to reflect divergences in the patterns of price movements for different types of properties.

Stratification involves constructing separate median price series for each subset – or “stratum” – of the data set and then aggregating up. Strata are typically defined by existing housing submarkets, such as property type and location.

The ability of stratified series to control quality without the use of complex statistical analysis is a major advantage of this method.

Education / Methodology

The median price series is constructed by taking the median price of all property transactions in a given area and time period. That is, if all sales in a given area and time period were sorted by their price, the middle sale price in each period forms the median price series. This measure is different to the average sales price in that average prices consider the values of all sales, whereas median prices consider all sales but are not affected by extremely high or low values (Mark and Goldberg, 1984).

The median price series is a straightforward measure of general price movements, but is affected by the quality of properties that sell between periods. One method for overcoming this is stratification (Rossini, 2002). For residential units, a stratified index which groups suburbs based on their long term median sales price is used, following the methodology outlined by Prasad and Richards (2007). Specifically, the long term median price (i.e. the median sales price achieved over a number of years) for every suburb is obtained. Suburbs are then ranked by this median price, and are assigned to strata by their rank. For each stratum, a separate median price series is calculated, as already described, An average of price levels at each time period is then estimated to form the stratified price series.

For residential houses a similar stratified model is used, but suburbs are grouped by their long term median “price-of-land.” That is, an estimate of land-value is obtained as sale price divided by land-size. This is then used to form the long-term price-of-land for each suburb, from which strata are created.