Methodological contribution to the detection of backward linkages between sectors of the economy

In national accounting, there are several synthetic indicators derived from the Leontief inverse, referred to as Total Material Requirement coefficients, which are commonly used in efficiency analyses and are known as input-output multipliers. Among the many indices that can be elaborated from input-output analysis, those related to the detection of key sectors are of special relevance since measuring the importance of a productive sector is especially relevant for policymakers when facing the need to make decisions to promote economic growth. There are two main alternative methods to identify key economic sectors, namely the Classical Multiplier method and the Hypothetical Extraction method (HEM), which essentially differ on the role of internal effects (the impact experienced by the sector in question). While the Classical method quantifies these internal effects, the HEM considers only the external impact. The latter method enables calculating backward linkages by isolating the column corresponding to demand-side sectors. However, such an alteration of the economic system can seem unrealistic and may give rise to doubts as to whether the results are biased, which in turn would cause incorrect public investment and false sectoral priorities. This paper offers an alternative method to detect key sectors based on a normalization of the Leontief inverse. After discussing the properties of the proposed standardization, the HEM, the Classical Multiplier method, and the one proposed here, are formally and empirically compared by using the 2010 input-output tables for Poland and Spain. The findings indicate that distinguishing and disaggregating the external effects from those that are purely internal has relevant policy implications. This disaggregation can be achieved through the proposed methodology, while avoiding the criticisms mentioned regarding the HEM, and with less effort required to calculate it.