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

Raïmi Aboudou Essessino; Guy Degla

doi:doi:10.11648/j.ml.20190504.12

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

Raïmi Aboudou Essessino, Guy Degla

Published in Mathematics Letters (Volume 5, Issue 4)

Received: 26 December 2019 Accepted: 8 January 2020 Published: 21 January 2020

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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.

Published in	Mathematics Letters (Volume 5, Issue 4)
DOI	10.11648/j.ml.20190504.12
Page(s)	47-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

National Accounts Disaggregation, Gross Domestic Product Quarterly Disaggregation, Denton Proportional Method, Generalized Denton Proportional Method, Multiobjective Quadratic Programming

References

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[2]	Ana, A., Enrique M. Q.: Software to perform temporal disaggregation of economic time series. Working paper and studies, ISSN 1725-4825, ISBN 92-894-8626-0, Luxembourg: Office for Official Publications of the European Communities, 3-40 (2005). http://europa.eu.int.
[3]	Ankur, S., Pekka, M., Kalyanmoy, D.: A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications. arXiv: 1705.06270v1 [math. OC] 17 May 2017, 4-7 (2017).
[4]	Aravind, S.: A Fast Elitist Multiobjective Genetic Algorithm: NSGA-II. Mathlab source code (2012). http://www. mathworks. com/matlabcentral/fileexchange/10429-nsga-iia-multi-objective-optimization-algorithm/content.
[5]	Christoph, Sax., Peter, S.: Temporal Disaggregation of Time Series. Contributed research articles, The R Journal Vol. 5/2, December 2013. ISSN 2073-4859, 80-81 (2013), https://journal.r-project.org/archive/2013-2/sax-steiner.pdf.
[6]	Di Fonzo, T., Marco, M.: On the Extrapolation with the Denton Proportional Benchmarking Method. IMF Working Paper Series, WP/12/169, 5-6 (2012), https://www.imf.org/external/pubs/ft/wp/2012/wp12169.pdf.
[7]	European Communities, United Nations and al.: System of National Accounts 2008. All rights reserved, New York, 1-7, 39-66, 295-315 (2009), https://unstats.un.org/unsd/nationalaccount/docs/sna2008.pdf.
[8]	Fonds Monétaire International: Manuel des comptes nationaux trimestriels: concepts, sources statistiques et compilation. Compilation de Adriaan M. B., Robert J. D., Nils O. Fonds Monétaire International, Washington, D.C., 93-139 (2001), https://www.imf.org/~/media/Websites/IMF/imported-publications-loe-pdfs/external/pubs/ft/qna/2000/textbook/fra/text.ashx.
[9]	International Monetary Fund: Quarterly National Accounts Manual. 2017 Edition, Pre-Publication, november 2018, 86-126, (2018), https://www.imf.org/external/pubs/ft/qna/.
[10]	Fréderic, B.: Optimisation continue, Cours et problème corrigé. Sciences Sup, Maths. Appl. pour le Master/SMAI, 327 pages Dunod, Paris, 20-21 (2006).
[11]	Julien, C.: Analyse post-Pareto en Optimisation Vectorielle Stochastique et Déterministe: Étude Théorique et Algorithmes. Thèse de doctorat, Mathématiques, Université de la Nouvelle-Calédonie, 19 (2014), https://tel.archives-ouvertes.fr/tel-01337505/document.
[12]	Marco M.: Nowcasting Annual National Annual National Accounts with Quarterly Indicateor: An Assessment of Widely Used Benchmarking Methods. IMF Working Paper. WP/16/71, march 2016, https:/www.imf.org/external/pubs/ft/wp/2016/wp1671.pdf.
[13]	Raïmi Aboudou Essessinou, Guy Degla and Babacar Mbaye Ndiaye: From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series. Journal of Advances in Mathematics and Computer Science, 34 (1 & 2): 1-15, 2019; Article no. JAMCS.51632, http://www.journaljamcs.com/index.php/JAMCS/article/view/30199.
[14]	Saleh A. R. Al-Mazel, Falleh R. M. Al-Solamy, Qamrul H. Ansari: Fixed Point Theory, Variational Analysis and Optimization. CRC Press, Taylor and Francis Group, A CHAPMAN & HALL BOOK, Pages 273−334.
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Raïmi Aboudou Essessino, Guy Degla. (2020). A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Mathematics Letters, 5(4), 47-53. https://doi.org/10.11648/j.ml.20190504.12

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ACS Style

Raïmi Aboudou Essessino; Guy Degla. A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Math. Lett. 2020, 5(4), 47-53. doi: 10.11648/j.ml.20190504.12

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AMA Style

Raïmi Aboudou Essessino, Guy Degla. A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Math Lett. 2020;5(4):47-53. doi: 10.11648/j.ml.20190504.12

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@article{10.11648/j.ml.20190504.12,
  author = {Raïmi Aboudou Essessino and Guy Degla},
  title = {A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product},
  journal = {Mathematics Letters},
  volume = {5},
  number = {4},
  pages = {47-53},
  doi = {10.11648/j.ml.20190504.12},
  url = {https://doi.org/10.11648/j.ml.20190504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20190504.12},
  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.},
 year = {2020}
}

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TY  - JOUR
T1  - A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product
AU  - Raïmi Aboudou Essessino
AU  - Guy Degla
Y1  - 2020/01/21
PY  - 2020
N1  - https://doi.org/10.11648/j.ml.20190504.12
DO  - 10.11648/j.ml.20190504.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 47
EP  - 53
PB  - Science Publishing Group
SN  - 2575-5056
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AB  - 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.
VL  - 5
IS  - 4
ER  -

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Author Information

Raïmi Aboudou Essessino
Guy Degla

Institute of Mathematics and Physics Sciences (IMSP), University of Abomey-Calavi (UAC), Dangbo, Benin

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APA Style

Raïmi Aboudou Essessino, Guy Degla. (2020). A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Mathematics Letters, 5(4), 47-53. https://doi.org/10.11648/j.ml.20190504.12

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ACS Style

Raïmi Aboudou Essessino; Guy Degla. A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Math. Lett. 2020, 5(4), 47-53. doi: 10.11648/j.ml.20190504.12

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AMA Style

Raïmi Aboudou Essessino, Guy Degla. A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product. Math Lett. 2020;5(4):47-53. doi: 10.11648/j.ml.20190504.12

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@article{10.11648/j.ml.20190504.12,
  author = {Raïmi Aboudou Essessino and Guy Degla},
  title = {A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product},
  journal = {Mathematics Letters},
  volume = {5},
  number = {4},
  pages = {47-53},
  doi = {10.11648/j.ml.20190504.12},
  url = {https://doi.org/10.11648/j.ml.20190504.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20190504.12},
  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.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product
AU  - Raïmi Aboudou Essessino
AU  - Guy Degla
Y1  - 2020/01/21
PY  - 2020
N1  - https://doi.org/10.11648/j.ml.20190504.12
DO  - 10.11648/j.ml.20190504.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 47
EP  - 53
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20190504.12
AB  - 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.
VL  - 5
IS  - 4
ER  -

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