Macroeconomists are used to work with the notion of an economy’s overall price level. When this price level increases over time, they describe this as inflation. The measurement of such price level changes requires suitable statistical techniques. Unfortunately, most macroeconomists leave the development of adequate solutions to price statisticians. Among those, however, there is widespread agreement that the notion of an economy’s overall price level is a meaningless concept. For macroeconomists, this finding has troubling implications: The development and use of macroeconomic models that are based on the notion of an overall price level is a waste of time.
When the notion of an overall price level is a flawed concept, then it would be equally flawed to define inflation as the increase of the overall price level. Therefore, price statisticians usually define inflation in an alternative way. In a first step, they compute for each individual commodity the individual price change. Then they take an average of these individual price changes. If this average indicates an overall price increase, then they denote this phenomenon as inflation.
The described contradiction between macroeconomics and price statistics can be traced back to two major works of Irving Fisher. In Fisher’s (1911) macroeconomic contribution “The Purchasing Power of Money” he develops his famous quantity theory of money. In this theory, the notion of an overall price level plays a pivotal role. Fisher’s (1922) price statistical contribution “The Making of Index Numbers” turns decidedly against the notion of an overall price level.
The contradiction between the macroeconomic and price statistical concepts of Fisher has survived well into the macroeconomics and price statistics of today. An elegant and simple attempt to avoid this inconsistency has been proposed by Warburton (1953, p. 360). He reformulates the equation of exchange (the central piece of Fisher’s quantity theory of money) in terms of intertemporal changes, thereby avoiding the concept of an overall price level. Since most macroeconomic models, however, are still based on the notion of an overall price level, the macroeconomists are still in need of a satisfactory justification for using this notion and they still desire a price index formula that is based on the change of price levels rather than on the average of individual price changes. This study attempts to meet both desires.
The study begins with a brief and critical discussion of the price statistical objections raised against the macroeconomists’ notion of price levels and price level changes. Beginning with Section 3, it proceeds to develop a price index formula that is based on the change of price levels. Some general guidance in this direction was already given by Fisher (1911, p. 202). Along these lines, Davies (1924, p. 183 ff) developed a workable price index formula. Unfortunately, his contribution did not receive the attention it deserved. The present study attempts to make up for this lapse. The starting point is the unit value index. However, for measuring the change in a price level, this simple index formula cannot be directly applied. Therefore, in Section 3 the concept of the amended unit value index is introduced. This type of price index can be employed in the context of homogeneous or almost homogeneous goods though not in the context of heterogeneous goods. The latter requires an additional refinement. This refinement leads to the family of generalized unit value indices. This index family is developed and explained in Section 4. A comparison with the traditional index formulas (e.g., Fisher index) can be found in Section 5. The axiomatic properties of the generalized unit value indices are explored in Section 6 and compared to those of the Laspeyres, Paasche, Fisher, Walsh, and Marshall-Edgeworth index. Section 7 provides some concluding remarks.
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