Editing Price index (section)

== Quality change ==
Price indices often capture changes in price and quantities for goods and services, but they often fail to account for variation in the quality of goods and services. This could be overcome if the principal method for relating price and quality, namely [[hedonic regression]], could be reversed.<ref>[http://www.techmatt.com/techmatt/Commercial_Knowledge_On_Innovation_Economics.pdf Commercial Knowledge Delivers This]</ref> Then quality change could be calculated from the price. Instead, statistical agencies generally use ''matched-model'' price indices, where one model of a particular good is priced at the same store at regular time intervals. The matched-model method becomes problematic when statistical agencies try to use this method on goods and services with rapid turnover in quality features. For instance, computers rapidly improve and a specific model may quickly become obsolete. Statisticians constructing matched-model price indices must decide how to compare the price of the obsolete item originally used in the index with the new and improved item that replaces it. Statistical agencies use several different methods to make such price comparisons.<ref>Triplett (2004), 12.</ref>

The problem discussed above can be represented as attempting to bridge the gap between the price for the old item at time t, <math>P(M)_{t}</math>, with the price of the new item at the later time period, <math>P(N)_{t+1}</math>.<ref>Triplett (2004), 18.</ref>

* The ''overlap method'' uses prices collected for both items in both time periods, t and t+1. The price relative <math>{P(N)_{t+1}}</math>/<math>{P(N)_{t}}</math> is used.
* The ''direct comparison method'' assumes that the difference in the price of the two items is not due to quality change, so the entire price difference is used in the index. <math>P(N)_{t+1}</math>/<math>P(M)_t</math> is used as the price relative.
* The ''link-to-show-no-change'' assumes the opposite of the direct comparison method; it assumes that the entire difference between the two items is due to the change in quality. The price relative based on link-to-show-no-change is 1.<ref>Triplett (2004), 34.</ref>
* The ''deletion method'' simply leaves the price relative for the changing item out of the price index. This is equivalent to using the average of other price relatives in the index as the price relative for the changing item. Similarly, ''class mean'' imputation uses the average price relative for items with similar characteristics (physical, geographic, economic, etc.) to M and N.<ref>Triplett (2004), 24–6.</ref>