John A. Sawyer

Linear Programming Estimates of Changes in Input Coefficients

THE purpose of this study is to develop a procedure for estimating changes in the coefficients of an inter-industry input-output matrix. Every attempt to prolong the useful life of such a set of coefficients carries an obvious practical interest. We desire to find a procedure which does not call for large quantities of supplementary data, and which does not require more than a reasonable volume of calculations.1 The method is applied to a sixteen-industry Canadian input-output matrix for the year 1949.2 This matrix is an aggregation of the forty-two-industry table published by the Dominion Bureau of Statistics.3 The adjustment of the coefficients (i.e., their up-dating) is done for 1956. Thus, the objective of the study is to estimate the 1956 matrix of input coefficients. Projections of the output of each of the sixteen industries for the years 1950-59 using the unadjusted 1949 matrix of input coefficients and estimates of the actual final demand for these years produce discrepancies between the projected outputs and estimates of actual output which quickly become too large to be tolerated. The projection errors for 1957-59 are shown in columns 3, 7, and 11 of Table I, where the 1949 matrix is referred to as matrix A.4 It

Forecasting with Input–Output Matrices: Are the Coefficients Stationary?

The incorporation of an input–output matrix into a macroeconomic forecasting model is a common practice. Are the input–output coefficients stationary, however? This study uses a set of 27 annual input–output matrices for Canada for the period 1961-87 to explore this question. It is found that, for 64 major coeficients for goods-producing industries, the majority have time trends with autocorrelated deviations from trend. In many cases the trend can be explained by relative price variations or by the movement of income per person. It is also found that, contrary to an earlier study, value coeficients are no more stable than are volume coeficients. It is recommended that this time series behaviour of input–output coefficients be taken into account when forecasting.