Leontief believed that the economy could be broken down into sectors, like farming, steel manufacturing, retailing, and so forth. Each sector uses material and services from other sectors to produce material or a service, which it supplies to those other sectors. This interrelationship can be described in the form of a mathematical matrix. It is often called an “input-output analysis.” When he first began investigating this model at the end of World War II, Leontief went to the Bureau of Labor Statistics to help gather the data he needed. To assist him, the bureau assigned a young analyst who was working there at the time, Jerome Cornfield.
Leontief could break the economy down into a few broad sectors, such as putting all manufacturing in one sector, or he could subdivide the sectors into more specific ones. The mathematical theory of input-output analysis requires that the matrix that describes the economy have a unique inverse. That meant that the matrix, once assembled, had to be subjected to a mathematical procedure called “inverting the matrix.” At that time, before the widespread availability of computers, inverting a matrix was a difficult and tedious procedure on a calculator. When I was in graduate school, each of us had to invert a matrix- I suspect as a kind of rite of passage “for the good of our souls.” I remember trying to invert 5 x 5 matrix and taking several days, most of which I spent locating my mistakes and redoing what I had done wrong.
Leontief’s initial set of sectors led to a 12 x 12 matrix, and Jerry Cornfield proceeded to invert that 12 x 12 matrix to see if there was a unique solution. It took him about a week, and the end result was the conclusion that the number of sectors had to be expanded. So, with trepidation, Cornfield and Leontief began subdividing the sectors until they ended with the simplest matrix they thought would be feasible, a 24 x 24 matrix. They both knew this was beyond capacity of a single human being. Cornfield estimated that it would take him several hundred years of seven-day work weeks to invert a 24 x 24 matrix.
During World War II, Harvard University had developed one of the first, very primitive computers. It used mechanical relay switches and would often jam. There was no longer any war work for it, and Harvard was looking for applications for its monstrous machine. Cornfield and Leontief decided to send their 24 x 24 matrix to Harvard where its Mark I computer would go through the tedious calculations and compute the inverse. When they sought to pay for this project, the process was stopped by the accounting office of the Bureau of Labor Statistics. The government had a policy at the time; it would pay for goods but not for services. The theory was that the government had all kinds of experts working for it. If something had to be done, there should be someone in government who could do it.
They explained to the government accountant that, while this was theoretically something that a person could do, no one would be able to live long enough to do it. The accountant was sympathetic, but he could not see a way around the regulation. Cornfield then made a suggestion. As a result, the bureau issues a purchase order for capital goods. What capital goods? The invoice called for the bureau from Harvard “one matrix, inverted.”
Source: The Lady Tasting Tea: How Statistics Revolutionized Science In The Twentieth Century, By David Salsburg, pp.177-78
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