A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product

Abstract

The estimation of a quarterly Gross Domestic Product (GDP) using an indirect approach based on quarterly indicators is often done by quarterly disaggregation of the national accounts branch per branch. The proportional method proposed by Denton (1971) leads to solving several optimization programs and doesn’t take into account the links between branches when searching for a quarterly GDP through indirect approach. This paper proposes a brand new approach to quarterly disaggregation of a GDP broken down into several branches or sectors, that takes into account the links between this branches. This approach generalizes the Denton (1971) proportional method and is an integrated approach in which the quarterly disaggregation of GDP is formulated as a multiobjective optimization problem. In fact, we group together on the one hand, all the elementary objective functions identified with respect to the various branches, and on the other hand, all the prescribed constraints according to the branches. Our technique relies on the minimization (in the least squares sense) of the difference in adjustment from neighbouring quarters under constraints provided by the annual benchmark data. The proposed model can be applied to the national accounts of any country using any approach for GDP compilation and it also takes also into account the usual inter dependence of its branches lacking in Denton method. Besides, it is worth noting that an algorithmic method needs to be devised due to the large scale of concrete GDP disaggregation problems.