Theory of the Price Index: Fisher¿s Test Approach and Generalizations

We wish to thank Georg Hasenkamp for valuable comments on an earlier draft of the manuscript and Steven Diamond for his kindness in reading the manu­ script and providing advice regarding the style of the exposition. We are also grateful to Miss Ingeborg Kasper for her careful typing of the manu­ script. Contents 1. Introduction 4 2. Price Indices Depending only on Prices 2. 1 Definition, Examples, Implications 4 2. 2 Characterizations of Pri~e Indices 15 3. Price Indices Depending on Prices and Quantities 22 3. 1 Definition, Examples 23 3. 2 Fisher's System of Tests 29 3. 3 Implications and Characterizations 35 3. 4 Independence and Inconsistency of Fisher's Tests 44 3. 5 General Solution of the Inconsistency Problem 54 4. Price Levels, Price Indices, and Fisher's Equation 59 of Exchange 4. 1 Definition, Examples, Implications 60 4. 2 Characterizations of Price Levels 64 4. 3 Fisher's Equation of Exchange Reconsidered 72 Bibliography 5. 83 6. Index 88 1. Introduction In the face of the economic, political, and social problems resul­ ting from world-wide inflation, theories of the price index have gained new attention. This newfound interest in price indices stems from the fact that all such indices are designed to serve as yardsticks for measuring the price behavior of goods and services. That is, all price indices relate to the concept of the 'purchasing power of money'. If prices increase, then the value of the unit of money declines, i. e.