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How used-car price changes are measured in the CPI

Purchase of second-hand motor cars (or used cars) had an expenditure weight of 3.30 percent of the Consumers Price Index (CPI) at the June 2006 quarter, making it one of the more highly weighted of the goods and services in the basket. 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. This article outlines how the CPI used cars index is compiled.

Position in CPI structure

The following table shows that the second-hand motor cars class falls within the transport group of the New Zealand Household Expenditure Classification used for the CPI.

Group, subgroup or class Level June 2006 expenditure weight (percent)
Transport Group 17.24
Purchase of vehicles Subgroup 5.24
Purchase of second-hand motor cars Class 3.30

 

The June 2006 quarter weight for the purchase of second-hand motor cars (3.30 percent) is higher than that for the purchase of new motor cars (1.69 percent). The expenditure weight allocated to the purchase of new cars represents gross expenditure on new cars for private use by households. The expenditure weight for purchase of second-hand cars, derived from the Household Expenditure Survey, represents net purchases of second-hand cars (that is, purchases of second-hand cars minus sales and trade-ins of second-hand cars, including trade-ins on purchases of new cars).

Price collection

Used-car prices and related information are collected quarterly from dealers via a postal questionnaire.

The current sample consists of about 300 used-car dealers located in the 15 CPI urban areas. Respondents are asked to provide information on every used car sold to households in the middle month of the quarter. Respondents are asked to exclude cars sold to businesses and other dealers, as those sales are out of scope of the CPI.

Information collected on each sale includes:

  • make
  • model
  • whether or not a used import, station wagon or automatic
  • year of manufacture
  • engine size
  • odometer reading (km)
  • price (agreed transaction price including GST, before any trade-in).

From time to time, respondents in the sample may need to be replaced (for example, due to closure of business). When this happens, another dealer is selected from the same area to replace the outgoing respondent.

Editing and data capture

Information supplied by respondents is subjected to a range of edits. Transactions that are not considered to be representative of household purchases are excluded.

Sales are not captured in the computer processing system if:

  • the car is more than 10 years old
  • the odometer reading is under 1,000km or over 200,000km
  • the vehicle is of a commercial type, such as a van or utility vehicle
  • the price is less than $100, or is $100,000 or more.

After information relating to all eligible sales has been captured in the computer processing system, consistency checks are performed to identify outliers and possible errors. Once editing and data capture has been completed, a final dataset is produced for use in the estimation phase.

Estimation

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 New Zealand uses a statistical technique called hedonic regression to calculate the price index for used cars. The method was implemented in the September 2001 quarter, replacing the previously used 'cell estimation' method, which had limitations such as making use of only some of the reported sales and not making use of odometer readings.

The regression model is stratified into five broad CPI regions (Auckland, Wellington, Rest of North Island, Christchurch and Rest of South Island) and a price index is calculated for each region. The regional indexes are then weighted together, by population share, to produce the national price index for used cars.

A used car is seen as comprising a bundle of characteristics. Once the characteristics in the bundle have been identified and measured, the hedonic function can be interpreted as breaking down the price of the car 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.

Each quarter, actual transaction prices and the following price-determining characteristics are collected from dealers in the CPI survey:

  • age of car
  • engine size
  • odometer reading
  • make and model.

Each quarter, sales information collected for the past eight quarters is fitted to a hedonic regression parameter model, along with information about the CPI urban area and the sale quarter. The model estimates price as a linear function of the following parameters:

The modelled price for quarter t = median age x age parameter + median engine size x engine size parameter + median odometer reading x odometer reading parameter + average make&model parameter + average CPI urban area parameter + parameter for quarter t

The index number for quarter t = (modelled price for quarter t / modelled price for period 0) x 1000.

Each quarter, the movement in each regional index from the previous quarter to the current quarter (based on data for the eight quarters to the current quarter) is linked to the index for the previous quarter (based on data for the eight quarters to the previous quarter).

Back to Price Index News: July 2007

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