5. Basic Index Number Theory A. Introduction

The answer to the question what is the Mean of a given set of magnitudes cannot in general be found, unless there is given also the object for the sake of which a mean value is required. There are as many kinds of average as there are purposes; and we may almost say, in the matter of prices as many purposes as writers. Hence much vain controversy between persons who are literally at cross purposes. 15.1 The number of physically distinct goods and unique types of services that consumers can purchase is in the millions. On the business or production side of the economy, there are even more products that are actively traded. The reason is that firms not only produce products for final consumption , they also produce exports and intermediate products that are demanded by other producers. Firms collectively also use millions of imported goods and services, thousands of different types of labor services, and hundreds of thousands of specific types of capital. If we further distinguish physical products by their geographic location or by the season or time of day that they are produced or consumed, then there are billions of products that are traded within each year in any advanced economy. For many purposes, it is necessary to summarize this vast amount of price and quantity information into a much smaller set of numbers. The question that this chapter addresses is the following: How exactly should the microeconomic information involving possibly millions of prices and quantities be aggregated into a smaller number of price and quantity variables? This is the basic index number problem. 15.2 It is possible to pose the index number problem in the context of microeconomic theory; that is, given that we wish to implement some economic model based on producer or consumer theory , what is the best method for constructing a set of aggregates for the model? However, when constructing aggregate prices or quantities, other points of view (that do not rely on economics) are possible. Some of these alternative points of view will be considered in this chapter and the next chapter. Economic approaches will be pursued in Chapters 17 and 18. 15.3 The index number problem can be framed as the problem of decomposing the value of a well-defined set of transactions in a period of time into an aggregate price multiplied by an aggregate quantity term. It turns …