Partial Subindexes of Input Prices: The Case of Computer Services

Abstract

A frequent lament of economists concerns the poor fit between available price statistics and those price index numbers required for analysis. Economists have recognized for quite some time, as in Moorsteen [17], that input price indexes and output price indexes are both useful constructions. For the most part regularly published price indexes are, if they have a theoretical foundation, industrial output price indexes, indexes of labor input costs, or approximations to true-cost-of-living indexes. Here we explore the construction of an input price index for capital services. The specific example we consider is an input price index of computer services, a of the prices of all inputs. While there are some peculiarities associated with computers which affect our study, the methodology involved in producing the appropriate has general application. An index of the prices of the services of a heterogeneous subset of capital goods which is independent of the prices of other factor inputs is called, using the terminology of Pollak [19], a partial subindex of input prices. Such an invariant will not always exist. Solow [22] and Hall [15] have shown, as Berndt and Christensen [2], under the assumption of constant returns to scale in the underlying production function, and the assumption that the total output produced is the sum of the outputs produced on the capital stocks of the various vintages, that this price index exists if and only if an invariant aggregate index of the stock of these capital goods exists. Fisher [10; 11] has shown that this invariant capital aggregate exists, maintaining these two assumptions, if and only if the differences between the various vintages of capital of which the aggregate is to be formed are capital-augmenting. That is, the production function must be of the form