OFR-24-89 The Effects Of Economic Growth, Technology Change, Consumption Pattern Change And Foreign Trade On Domestic Demand For Primary Metals. 1963-82 ? Appendix A & B ? Appendix A - Technical Description Of Procedures

This appendix documents the mathematical approach to deriving the components of change presented in this report. The formulation closely follows that contained in Chapter IV of the documentation for the BEA 1977 Input-Output Tables.' The basic elements for the calculations include the "use" matrix (U), the "make" matrix (M), and any of the ten columns of final demand (generically represented by the symbol y). The use matrix contains information about changes in the technological processes of production, while the make matrix describes the nature of secondary product production in each industry. We adhere to BEA conventions in maintaining careful distinctions between commodity output (c) and industry output (x). The industry-by-industry 1-0 tables supplied by NYU for use in this analysis are square matrices, with the number of commodities and the number of industries both equal to 85. The BLS table for 1982 (commodity by industry) was aggregated and adjusted to be consistent with the earlier tables. The three basic steps for estimating components of change proceed as follows for each column of final demand. 1) Calculate the actual change in output of each commodity for each of the four time periods: 1963-72, 1972-77, 1977-82, and 1963-82.