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. The problem discussed above can be represented as attempting to bridge the gap between the price for the old item at time t, , with the price of the new item at the later time period, . The overlap method uses prices collected for both items in both time periods, t and t+1. The price relative / 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. / 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. 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. See also List of price index formulas Aggregation problem Inflation Chemical plant cost indexes GDP deflator Etienne Laspeyres Hermann Paasche Hedonic index Indexation Irving Fisher Real versus nominal value (economics) U.S. Import Price Index Volume index References Further reading Chance, W.A. "A Note on the Origins of Index Numbers", The Review of Economics and Statistics, Vol. 48, No. 1. (Feb., 1966), pp. 108–10. Subscription URL Diewert, W.E. Chapter 5: "Index Numbers" in Essays in Index Number Theory. eds W.E. Diewert and A.O. Nakamura. Vol 1. Elsevier Science Publishers: 1993. (Also online.) McCulloch, James Huston. Money and Inflation: A Monetarist Approach 2e, Harcourt Brace Jovanovich / Academic Press, 1982. Triplett, Jack E. "Economic Theory and BEA's Alternative Quantity and Price indices", Survey of Current Business April 1992. Triplett, Jack E. Handbook on Hedonic Indexes and Quality Adjustments in Price Indexes: Special Application to Information Technology Products. OECD Directorate for Science, Technology and Industry working paper. October 2004. U.S. Department of