Measurement of Statistical Errors, Iteration Algorithms and Convergence Speed in Updating Coefficient and Transaction Matrices

Abstract

During thepast six decades, the analysts of the input – output economics(IOE) have used two approaches of input – output coefficient matrix(IOCM) and intermediate transactions matrix(ITM), both of which are based on iteration algorithms, in updating input – output tables(IOTs). The former is theoretically based on the production function and is more popular as compared with the latter which is only in terms of accounting. The challenging issue for the analysts of IOE is similar or different results of the two approaches. A group insists on different results, whereas, the observations of another group suggest that the results are equivalent. Neither of the mentioned groups consider factors such as aggregation and convergence speed with respect to the number of iterations in algorithms of the two approaches. The main focus of this article is to investigate the theoretical and empirical aspects of factors, using two survey-based symmetric IOTs of Iran for the years 1996 and 2001. With respect to the above factors, the 3 sectors, 7 sectors, 15 sectors and 21 sectors are considered. This article concludes two overall findings: a 1-statistical error in the two approaches exits but insignificant. 2-The convergence speed with lower number of iterations in the IOCM approach is higher than that of the second approach.

Keywords

• ras method
• input – output coefficient matrix
• intermediate transactions matrix
• statistical errors