In the June 2011 quarter, Statistics New Zealand will implement an improved hedonic formulation for the second-hand motor cars (or used cars) component of the consumers price index (CPI).
Measuring price change for used cars presents some particular challenges. Unlike new cars, where prices can be observed from one quarter to the next for the same sample of makes and models, each used car sale is in some respects unique. For example, an agreed transaction price for a particular used car would reflect factors such as the age of the car and its mileage. The mix of makes, models, ages, and odometer readings of used cars sold by dealers in the CPI sample varies from one quarter to the next. To measure price change, these differences must be controlled for.
Statistics NZ uses a statistical technique called hedonic regression to calculate the price index for used cars. The method was implemented in the September 2001 quarter. A used car is seen as comprising a bundle of characteristics. Once these characteristics are identified and measured, the hedonic function can be interpreted as breaking down the car’s price into the 'implicit' prices and quantities of the characteristics. The prices are referred to as implicit because they must be estimated rather than directly observed.
The existing hedonic estimation
For the hedonic estimation introduced for used cars in 2001 (Statistics New Zealand, July 2007), price is modelled against quarter, region, make and model, age of car, engine size (cc rating), and odometer reading, as shown in formula (1).
Where
Pc is the price of car c (note that there is no t term as we can assume each individual car is sold only once with the same characteristics)
Dct = 1 in the quarter t that car c is sold and 0 otherwise
The following characteristics K are included in the model for each car c sold:
- city/town of purchase (15 categories
- make and model (47 categories)
- age of car (in years)
- size of engine (cc rating, eg 2300)
- odometer reading (in kilometres).
The linear formulation was used initially as this made the hedonic index a more efficient version of the previous, estimation cell method.
Hedonic indexes are calculated for each of five broad regions of New Zealand (Auckland, Wellington, Rest of North Island, Christchurch, and Rest of South Island). These are weighted together, using population-based expenditure shares that are updated at the three-yearly CPI reviews, to get the national used cars index.
To operationalise the method, a rolling window of the latest eight quarters is used to estimate the hedonic model each quarter. The derived index for the most recent quarter is linked to the previous quarter's index number.
The new hedonic estimation
An improved hedonic formulation for used cars will be implemented in the June 2011 quarter CPI. At the same time, the production process will be streamlined to make it simpler and more robust.
The hedonic model has been updated as follows:
- price is now logged, which gives the model a better fit to the data
- a more detailed classification of make and model is incorporated – from 47 categories to 96
- squared terms have been added for age of car and size of engine
- an identifier for the used car dealer is now included.
The updated model is:
With Pc and Dct as for (1). Characteristics K are now:
- city/town of purchase (15 categories)
- make and model (96 categories)
- age (in years) and age squared
- size of engine and size of engine squared
- odometer reading
- dealer (approximately 300).
Now that the hedonic formulation has been optimised, there is potential for reducing the sample size, and hence the respondent load of the CPI used cars survey. Work is now underway to determine the minimum sample size required for an accurate estimation.
Along with redesigning the sample's size and allocation, representation of the price movements of used cars sold through auction and online needs to be considered when designing the sample. These channels are not included in the current sample.
Reference
Statistics New Zealand (July 2007). 'How used-car price changes are measured in the CPI’ Price Index News. Available from www.stats.govt.nz.
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