Estimating technological coefficients by the analytic hierarchy process

We give a summary and an example of a new, systems oriented, method for estimating the input-output coefficients of a given economy. Our approach is based on pairwise comparisons among the sectors of the economy ranking them according to their priority on a ratio scale[l]. What we obtain corresponds closely to what is computed by traditional methods, but a major advantage to hierarchical measurement is that it does not require extensive use of details to capture the significant relations among the sectors. We shall illustrate here that the general understanding one has about interactions in an economic system is often adequate for making estimates of input-output coefficients without the use of an enormous amount of data. This is particularly useful in cases where market prices do not provide a clear indication of the relative impacts of the various sectors. We wish to point out that the table obtained in this way should be interpreted as a first step in the estimation process and is not a substitute for what one can obtain by thorough and deep analysis by refined methods. However, when one is limited in time and resources and when sufficient data are unavailable, but still one needs an estimate, this is an effective approach and has rigorous underlying mathematical justification. We now summarize some of the main ideas of our approach. Measurement evolves out of comparisons, particularly pairwise comparisons. The scale most desired for the values it yields is the ratio scale (invariant under positive similarity transformations). Let us suppose that we have n objects A,, , A, whose vector of corresponding weights w = (w,, , w.) is known. Let us form the matrix of pairwise comparisons of weights