Una aplicación del modelo Leontief sobre la economía Española con técnicas big data

The Leontief model allows estimating production and has been used in a wide variety of problems, especially in markets that must be kept in balance, for example those that depend on energy materials. The mathematical intervention on the model consists of solving a matrix equation, which requires the calculation of the inverse of a matrix. It is known that in the case of large matrices this calculation is enormously complicated, due to the characteristics of the operations that must be carried out. We will use sparse matrix operations (large matrices stored efficiently) to calculate the inverse of the matrix obtained when considering all industrial companies in Spain. The resulting matrix, in this case, is not very dense, because companies usually have connections in nearby sectors. We will design a methodology that will allow us to estimate the production of a group of companies with real assumptions with a large amount of data. Also, we will show how it would be possible to make estimates about the submerged economy.