'엑셀(Excel) 2000'을 이용한 산업연관분석 계산의 성능실험

An Experiment on Computational Ability of the 'Excel 2000' in Input-Output Analysis

In the input-output analysis, which was devised by the late Professor Leontief, calculation of the inverse matrix [I-A]??¹(A is the input-output coefficient matrix) is the most essential. About 40 years ago, when Korea had no computer, it was impossible to calculate inverse of a 50 X 50 input-output matrix. At present, personal computers are becoming ever popular and powerful every year. It became so easy to calculate a large-size inverse matrix even with a desk-top personal computer. In this paper a computer experiment was done to see how fast an ordinary desktop personal computer can calculate an inverse of a 50 X 50 input-output coefficient matrix, and to see how stable the results are. Also, since the [I-A]??¹ can be expressed as a series of I + A + A² + A³ + ……, result of this indirect inversing was compared with that of the direct inversing to see how fast it converges. For the experiment, the year 1995 75-sector input-output table published by the Bank of Korea was aggregated into 50 sectors. This 50-sector experiment was chosen because the 'EXCEL 2000', one of the most popular software for personal computers can calculate inverse matrix of maximum 52 dimensions. Astonishingly, the EXCEL command to invert a matrix, 'MINVERSE', could invert the 50 X 50 input-output coefficient matrix in 0.033 second. This means that it can invert a 50 X 50 matrix roughly 30 times per second. It was also found that the results were very stable with the error limit of ±1.0*10-15. When the [I-A]-¹ was approximated by the series I + A + A² + A³ + ……, the term A8 became very small to have S = ∑∑aij less than 1. In conclusion, this experiment has shown that today's desk-top personal com-puter can be widely used for a large scale input-output analysis.