# Frequently Asked Questions about Hedonic Quality Adjustment in the CPI

- Why does the CPI adjust prices for changes in quality?
- What is hedonic quality adjustment?
- What items in the CPI are hedonically adjusted?
- How does the hedonic method estimate the value of quality change?
- Can you explain how the CPI uses the hedonic regression model to estimate and apply a quality adjustment?
- Would you walk through another example at a more detailed level?

#### Why does the CPI adjust prices for changes in quality?

The CPI measures the average change in price over time of consumption goods and services by following the prices of a representative sample of consumption items in the retail establishments that sell them. A fundamental problem for the goods and services in the CPI sample is that their characteristics, not just their prices, change over time as the retailers introduce new versions of items and discontinue the older versions. In many categories of items, this is the primary time when price change occurs. The new version of the item may provide additional benefits or, in some cases, reduced benefits. This change in benefit is quality change.

To measure price change accurately, the CPI must be able to distinguish the portion of price change due to this quality change. The traditional CPI solution to this problem is to temporarily remove an item from the sample when its quality has changed. While this method is sometimes acceptable, it biases the CPI if new version price changes are systematically different from the price changes of the unchanged goods.

#### What is hedonic quality adjustment?

Hedonic quality adjustment is one of the techniques the CPI uses to account for changing product quality within some CPI item samples. Hedonic quality adjustment refers to a method of adjusting prices whenever the characteristics of the products included in the CPI change due to innovation or the introduction of completely new products.

The use of the word “hedonic” to describe this technique stems from the word’s Greek origin meaning “of or related to pleasure.” Economists approximate pleasure to the idea of utility – a measure of relative satisfaction from consumption of goods. In price index methodology, hedonic quality adjustment has come to mean the practice of decomposing an item into its constituent characteristics, obtaining estimates of the value of the utility derived from each characteristic, and using those value estimates to adjust prices when the quality of a good changes.

The CPI obtains the value estimates used to adjust prices through the statistical technique known as regression analysis. Hedonic regression models are estimated to determine the value of the utility derived from each of the characteristics that jointly constitute an item.

#### What items in the CPI are hedonically adjusted?

The CPI uses hedonic quality adjustments in item categories that tend to experience a high degree of quality change either due to seasonal changes, as in apparel items, or because of innovative improvements and technological changes, as in consumer appliances and electronics.

See table for a complete list of items for which the CPI uses hedonic based quality adjustments to account for quality change.

#### How does the hedonic method estimate the value of quality change?

CPI data collectors obtain the price and a full description of each item in the CPI sample. In those item categories where the CPI uses the hedonic method, BLS economists use a statistical technique called regression modeling to estimate a value for each characteristic; these values sum to the price of the item. For instance, in the men’s shirts hedonic model, sleeve length is an estimated characteristic. The estimate for long sleeves is interpreted as the portion of the shirt’s price that can be attributed to the presence of long sleeves.

Hedonic models are estimated about every two years to capture new innovations in the marketplace, or to reflect changes to the value estimates of existing characteristics.

#### Can you explain how the CPI uses the hedonic regression model to estimate and apply a quality adjustment?

To illustrate the mechanics of a hedonic quality adjustment, it helps to begin with the generalized form of the hedonic regression equation:

(1)

Where the dependent variable, lnP, is the natural log of price, ß are the coefficients estimates of the independent variables (Xk), and e is the error term. The coefficients are a measure of the percentage change in price associated with a unit change in the characteristic. If the item being modeled is men’s shirts, the independent variables might be sleeve length and fiber composition; a simplified version of a hedonic model for men’s shirts might be:

(2)

Here all shirts are either short sleeve or long sleeve and either cotton/poly or 100% cotton. After doing the statistical processing BLS might estimate that ß1 = 0.15 and ß2 = 0.25. This indicates that a long sleeve shirt is 15 percent more valuable than a short sleeve one and that a 100% cotton shirt is 25 percent more valuable than a cotton/poly blend shirt.

If the BLS data collector is forced to replace a short-sleeve cotton/poly shirt in the CPI sample with a long sleeve 100% cotton shirt, the CPI would attribute 40 percent of their price difference to increased shirt value (15 percent for sleeve length and 25 percent for fiber). The CPI would treat the remaining 60 percent of the price difference as pure change.

If the price of the original shirt had been $20 and that of the replacement shirt $30, rather than using a $10 increase in price for that sample observation, the CPI would use a $6 increase, attributing the other $4 of the price difference to difference in the quality of the two shirts.#### Would you walk through another example at a more detailed level?

Here is an example of a hedonic regression model for televisions.

Televisions

Characteristic

CategoryCharacteristic

NameCoefficients P>T Statistics Intercept 3.4455 30.49 Display Type Projection -0.25586 -2.60 CRT Base - DLP 0.58356 8.58 LCD Projection 0.38566 5.43 LCD Direct View 0.73075 12.49 Plasma 0.72483 9.81 Screen Size 1 0.08348 11.24 Screen Size 2 -0.00049 -5.19 Features Picture-In-Picture 0.08430 2.39 Universal Remote 0.16261 4.42 High Def (HDTV) 0.34280 5.53 Extd Def (EDTV) 0.12228 1.82 3D Comb Filter 0.07122 1.47 Flat Screen 0.18461 3.91 S-Video Input 0.13772 2.08 VCR Built-In 0.18958 1.96 DVD Built-In 0.38247 5.33 From this model, we can see that LCD direct view and plasma televisions have prices that are about 70% greater than CRT televisions, all other characteristics being equal.

When an item is replaced and it is possible to apply the hedonic model, the CPI estimates what the price of the new version of item would have been if it had been in the CPI sample in the previous period. To obtain that estimate, the previous period price of the old version (which was observed) is adjusted using the value of the change in characteristics between the two versions.

Here’s an example of an item replacement:

Characteristics Item A Item B Price $250.00 $1,250.00 Features 27 Inch 42 Inch CRT Plasma EDTV HDTV S-Video Input S-Video Input Universal Remote Universal Remote Item A is a television that is no longer available and it has been replaced by a new television, Item B. The characteristics in bold differ between the two TVs. There is a large degree of quality change and there is a very large (400%) difference in the prices of these TVs. Rather than use the 400 percent increase in price between Item A and Item B, the quality adjusted rate of price change is measured by the ratio of the price of Item B in the current period ($1,250.00) over an estimated price of Item B in the previous period – Item B’.

To derive the estimated price of Item B’, we use the following equation:

(3) Where PB,t+s-1 is the quality adjusted price, PA,t+s-1 is the price of Item A in the previous period, and is the constant e, the inverse of the natural logarithm, exponentiated by the difference of the summations of the ßs for the set of characteristics that differ between items A and B. The exponentiation step is done to transform the coefficients from the semi log form to a linear form before adjusting the price.

For our television example, equation (3) looks like this:

(4)

When this quality adjustment is applied, the ratio of price change looks like this:

Characteristics Item A Item B Price $1,345.02 $1,250.00 Features 42 Inch 42 Inch Plasma Plasma HDTV HDTV S-Video Input S-Video Input Universal Remote Universal Remote The resulting price change is -7.1 percent after the quality adjustment is applied.

**Last Modified Date:** July 8, 2010