Multisectoral structures and policy design

In this article, an attempt is made to identify a convenient structure of a policy variable, the final demand vector, through the use of a multisectoral model. The method used relies on a specific spectral decomposition that allows for the quantification of the scale-effect of each structure that the policy variable can assume on the structures of the objective variable, the total output vector. This quantification is of aggregate type, since each scalar obtained is valid for all the sectoral components of both the policy variable and the objective variable. But, more relevant, they are consistent with the multisectoral feature of the model, overcoming the objections put forward by the theory of aggregation. In fact, the aggregation theory states that if we aggregate sectors, we obtain a new model with different structural properties, while, in our case, the aggregate scalars that we obtain for each structure are perfectly consistent with the original model. We call these scalars macroeconomic multipliers since they say how many times the modulus of the multisectoral policy variable is multiplied to obtain the modulus of the multisectoral objective variable. Once the structures and the associated macro multipliers are identified, the policy maker can have a complete picture of the economic structure of the objective variable that can be attained and determine a convenient structure of the policy variable choosing either one structure or a combination of the structures identified.