## Tuesday, May 18, 2010

### Lower bound problems of hedonic indices

Prices are a fundamental feature of modern economies, yet measuring a true price change is exceedingly difficult due to the constantly changing quality of goods and services. I have previously discussed the use of hedonic price indices, where adjustments are made for quality changes using regression techniques, and the potential pitfalls when interpreting the results of this method. I apologise for raising this issue again, but I hope to clarify my message with an example.

While a hedonic index is a useful tool, and when part of a package of price indices can clarify our understanding of price and quality movements, many unresolved issues persist. One issue that attracts little attention is how to interpret and apply results from hedonic price index calculations.

Today I want to further elaborate upon, and demonstrate using the table below, what I call the lower bound problem of hedonic price indices. Quality improvement does not imply that prices faced by consumers have dropped, especially if lower quality goods are no longer available. Buyers of cheaper products will not see the price declines measured by a hedonic index, and may even see price increases.

The above table has been constructed to show how different methods for determining price changes can produce significantly different results. This hypothetical market could be computers, cars, or any other market where quality changes noticeably over time.

The animal names are the models. For car markets, it could be Corolla, Landcruiser and so on, or for computers, Dell Latitude, Apple MacBook or any other model. The reason to include models is that one method for determining price changes is called the model-matching technique. Because models typically have fewer quality changes than the market as a whole, and that they typically represent a segment of the market (budget or premium), compiling prices over time for the same model can give a reasonable measure of price changes for similar quality products. In the table above two models are highlighted, Kangaroo and Echidna, to show how their prices have changed over the period. If we take the average price change of models we can match over the period (the model matching technique), we get a price change in this market of -42% over the eight-year period.

The number beside each model is a measure of quality. I have used a single number in this situation, but typically there would be a number of associated quality measures. You will note that the quality of each model improves over time, thus if we use a hedonic (quality controlled) method for measuring price change, it will show a more substantial price decline. If we were to buy a ‘quality level 9’ product in 2001 it would be $3,000, while in 2009 it would be$1,000 – a 67% decline in price.

Using a median price index, where quality is not considered, the data in this table shows a median price increase of 14% over the period (assuming an equal volume of sales in each price category). In this scenario, this measure more accurately shows the price movement of the market as a whole. If you wanted to stay at the same level in the market, this is the price change you would experience.

Finally, and this is the main pitfall when utilising quality-adjusted prices measures to make policy decisions, the price change for the lower bound market entrant has increased 33%. The cheapest computer/car/shoe/phone/appliance, or whatever good this happens to be, has gone up in price significantly while the quality-adjusted measures show large declines.

Measures such as the CPI (a price index) and the Analytical Cost of Living Indexes do consider quality change, yet we apply these measures as a way to adjust welfare payments, even though most welfare recipients will be lower bound market entrants for much of their consumption bundle.

In an ideal world, a selection of price indexes using different methods would be produced for each major consumption category to show paint a clear picture of the situation being faced by different members of society. Not only would we measure ‘pure price change’, but also changes to the cost of living which can more easily guide policymaking.