Robert E. Prasch
The earliest index numbers in economics were associated with attempts to theorize about the “general price level”. That the “general price level” was a distinct abstraction which existed as a quantifiable entity was a shared certainty of all the early theorists who constructed index number schemes. 1 The idea of a general level of prices, one which exists independently of relative prices, was a direct result of these theorists’ prior belief in the quantity theory of money.
The problem of index number construction is to establish a number for an abstract quantity (price level or total quantity) which cannot be observed or measured in practice. 2 A pronounced difficulty with economic data is that they consist of two distinct phenomena compounded into a single observation. One is the actual quantities of goods under consideration. The other is the set of prices associated with each of these goods. For example, a number such as $4.76 does not reveal much about a specific economic phenomenon. For such a number to make sense, we must first establish both the value of the currency unit and the temporal and spatial quality and quantity of goods being offered for sale. 3 In this example, the system is underdetermined in the mathematical sense, since we have only one equation with two unknowns: P x Q=$4.76. In simple language, this means that more information will be required before we can establish the numerical value of either P or Q.
In its most simple formulation, index number theory can be thought of as a technique or method. This method enables us, by a mental exercise, to assign a number, called an index number, to either P or Q. Such an expedient allows us to resolve the problem of underdetermination and solve for the other variable. The trick is to do this in a sensible manner which does not so completely distort reality that it results in a useless set of data. The next section of this chapter will discuss the different approaches that nineteenth-century theorists used to resolve the index number problem. In particular, the chapter will focus on the evolving understanding of the theory of probability and how this change resulted in different approaches to index number theory.