RDP 2006-04: Measuring Housing Price Growth – Using Stratification to Improve Median-based Measures 3. Stratification
May 2006
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The problems illustrated in Section 2 reflect the fact that the prices recorded in any quarter relate to only a sample and not the entire population of houses. This would not be a significant problem if the sample was a random sample from the population of all houses. Despite the significant number of transactions available each quarter, the results above suggest that the observed samples in any quarter are far from random. Given that there is no ex ante way of ensuring a random sample of housing transactions, the issue becomes one of dealing ex post with the non-randomness of the sample.
The measure for the change in house prices that is proposed in this paper uses mix-adjustment, which in turn uses stratification, to control for compositional change. Stratification is a commonly used technique because it can increase the precision of sample estimates (Hansen, Hurwitz and Madow 1953). Indeed, it is a method employed in measuring house prices in a number of countries (Table 3).[11] However, as is discussed in more detail below, the method that we use to stratify our sample differs significantly from most other applications in one respect.
Stratification involves dividing a population into groups (strata) such that observations within each group are more homogenous than observations in the entire population. Within each stratum, it then becomes more likely that an observed change in a characteristic of interest represents a true change rather than a spurious one due to compositional effects. Once strata have been defined, a measure of central tendency from each strata is weighted together to produce an aggregate price measure.
| Index provider | Variables used in mix adjustment |
|---|---|
| Australian Bureau of Statistics (ABS) | Region, percentage of three-bedroom houses within a region and an index of the social and economic conditions in a suburb |
| Hong Kong Monetary Authority | The saleable area of a dwelling |
| Urban Redevelopment Authority (Singapore) | Dwelling type and region, with prices quoted in per square metre terms |
| Bank of Canada/ Royal Le Page | Region and dwelling type |
| Deutsche Bundesbank/ Bulwien AG | Region and dwelling type |
| Ministerio de Formento (Spain) | Calculates the average price of a house per square metre. Distinguishes between dwellings based on location and size of municipalities |
| Hometrack (UK) | Postcode and dwelling type |
| Rightmove (UK) | Postcode and dwelling type |
| Office of the Deputy Prime Minister (ODPM, UK) | Region, locations within region, dwelling type, old or new dwelling and first or repeat-home buyer purchase. A hedonic equation is used to calculate the price for each strata. |
| Sources: ABS (2005); BIS database; various national sources | |
Traditionally, the variable which has been used to group transactions is geography (Table 3).[12] Defining housing strata based on geography captures the notion that dwellings in a given area share amenities linked to the property's location. In addition, the literature on housing submarkets finds that geographic variables are an important determinant of housing prices (see Bourassa et al 1999 and Goodman and Thibodeau 2003). Similarly, work using Australian data by the ABS (2005) and Hansen (2006) finds that location is a fundamental price-determining characteristic of dwellings. Another reason for grouping by location is a practical one; geographic variables are readily available in most databases of housing transactions (Goodman and Thibodeau 2003).
The increase in precision gained from stratification is dependent on how strata are defined. Hansen et al (1953) suggest that strata boundaries should be defined using information on all relevant variables that influence the characteristic being measured. Similarly, Lavallée (1988) notes that the most useful variables for stratifying data are those that are highly correlated with the variable of interest.
In the current case, we are particularly concerned about removing the noise in changes in median prices that results from the combination of compositional change and the extreme range in housing prices (the fact that prices of some houses in a city may be more than 10 times higher than the prices of other houses). For our exercise we have no particular interest in trends in house prices across different regions of a city. Furthermore, purely geographical stratification is unlikely to divide houses into strata with the maximal feasible similarity in prices within strata. Accordingly, we group houses and suburbs into strata based on the variable that is most likely on an a priori basis to explain the price in any transaction, namely the long-term level of prices for the suburb where the house is located.
Footnotes
See ABS (2005, pp 6–8) for some additional discussion of the use of stratification in house price measurement. [11]
In addition to location, most measures which use stratification also group transactions according to dwelling type. As well as the measures in the table, a number of countries in continental Europe (including Austria, Finland, Hungary and Portugal) make a rudimentary adjustment for quality by measuring prices in per square metre terms. Beyond this, most measures do not control for quality. This is probably because very few datasets contain comprehensive information on dwelling characteristics. [12]