Advertisement

Inverse Problems in Economic Measurements

  • A. A. Shananin
Article
  • 24 Downloads

Abstract

The problem of economic measurements is discussed. The system of economic indices must reflect the economic relations and mechanisms existing in society. An achievement of the XX century is the development of a system of national accounts and the gross domestic product index. However, the gross domestic product index, which is related to the Hamilton–Pontryagin function in extensive economic growth models, turns out to be inadequate under the conditions of structural changes. New problems of integral geometry related to production models that take into account the substitution of production factors are considered.

Keywords

gross domestic product economic growth model Hamilton–Pontryagin function Houthakker–Johansen model integral geometry Bernstein’s theorems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. S. Landefeld, “GDP: One of the great inventions of the 20th century,” Bureau of Economic Analysis, Survey of Current Business, January 2000.Google Scholar
  2. 2.
    D. Coyle, GDP: A Brief but Affectionate History (Princeton Univ. Press, Princeton, N. J., 2014).Google Scholar
  3. 3.
    E. Pestel, Beyond the Limits of Growth: A Report to the Club of Rome (Universe Books, New York, 1989).Google Scholar
  4. 4.
    N. N. Moiseev, Mathematics Sets Up and Experiment (Nauka, Moscow, 1979) [in Russian].Google Scholar
  5. 5.
    A. A. Petrov and I. G. Pospelov, “System analysis of developing economy. I–IV,” Izv. Akad. Nauk SSSR, Ser. Tekh. Kibern. No. 1–5 (1979).Google Scholar
  6. 6.
    Ph. Aghion and P. Howitt, Endogenous Growth Theory (MIT Press, Cambridge, Mass., 1998).MATHGoogle Scholar
  7. 7.
    R. Lucas and B. Moll, “Knowledge growth and the allocation of time,” J. Political Econ. 122 (1), 1–51 (2014).CrossRefGoogle Scholar
  8. 8.
    V. M. Polterovich and G. M. Khenkin, “Evolutionary model of economic growth,” Ekon. Mat. Metody 25 (3), (1989).Google Scholar
  9. 9.
    G. M. Khenkin and V. M. Polterovich, “Schumpeterian dynamics as a nonlinear wave theory,” J. Math. Econ., 551–590 (1991).Google Scholar
  10. 10.
    D. Acemoglu, Introduction to Modern Economic Growth (Princeton Univ. Press, 2009).MATHGoogle Scholar
  11. 11.
    The Stiglitz Report: Reforming the International Monetary and Financial Systems in the Wake of the Global Crisis: Report of the Commission of Experts of the President of the United Nations General Assembly on Reforms of the International Monetary and Financial System (New Press, New York, 2010).Google Scholar
  12. 12.
    J. E. Stiglitz, A. Sen, and J.-P. Fitoussi, Mis-Measuring Our Lives: Why GDP Doesn’t Add Up? The Report by the Commission on the Measurement of Economic Performance and Social Progress (New Press, New York, 2010).Google Scholar
  13. 13.
    A. A. Shananin, “The problem of integrability and the nonparametric method for the analysis of consimer demand,” Trudy MFTI 1 (4), 84–98 (2009).Google Scholar
  14. 14.
    A. A. Petrov and A. A. Shananin, “Integrability conditions, distribution of income, and the social structure of society,” Mat. Modelir. 6 (8), 105–125 (1994).MATHGoogle Scholar
  15. 15.
    N. I. Klemashev and A. A. Shananin, “Inverse problems of demand analyses and their applications to computation of positively-homogeneous Konus–Divisia indices and forecasting,” J. Inverse Ill-Posed Probl. 2, 367–391 (2016).MATHGoogle Scholar
  16. 16.
    A. A. Shananin, “On the aggregation of demand functions,” Ekon. Mat. Metody 25, 1095–1105 (1989).MathSciNetMATHGoogle Scholar
  17. 17.
    F. Talla Nobibon, L. Cherchye, Y. Crama, T. Demuynck, B. De Rock, and F. Spieksma, “Revealed preference tests of collectively rational consumption behavior: Formulations and algorithms,” KU LEUVEN, faculty of economics and business, 2013.Google Scholar
  18. 18.
    N. I. Klemashev and A. A. Shananin, “Estimating the complexity of verifying the temporary dictator hypothesis with a positively homogeneous utility function,” Trudy MFTI, No. 4, 17–27 (2015).Google Scholar
  19. 19.
    H. S. Houthakker, “The Pareto distribution and the Cobb-Douglas production function in activity analysis,” Rev. Econ. Studies, No. 60, 27–31 (1955-56).CrossRefGoogle Scholar
  20. 20.
    L. Johansen, Production Functions (North Holland, Amsterdam-London, 1972).MATHGoogle Scholar
  21. 21.
    W. Hildenbrand. “Short-run production functions based on micro-data,” Econometrica 49, 1095–1125 (1981).MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    A. A. Shananin, “Investigation of a class of production functions appearing in the macrodescription of economic systems,” Zh. Vychisl. Mat. Mat. Fiz. 24, 1799–1811 (1984).MathSciNetMATHGoogle Scholar
  23. 23.
    A. Cornwall, “A note on using profit functions,” Int. Econ. Rev. 14 (2), 211–214 (1973).CrossRefMATHGoogle Scholar
  24. 24.
    A. A. Shananin, “Investigation of a class of production functions appearing in the macrodescription of economic systems,” Zh. Vychisl. Mat. Mat. Fiz. 25, 53–65 (1985).MathSciNetGoogle Scholar
  25. 25.
    G. M. Henkin and A. A. Shananin, “Bernstein theorems and Radon transform: Application to the theory of production functions,” in Translation of mathematical monographs, vol. 81, 1990, V. 81, pp. 189–223.MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    G. M. Henkin and A. A. Shananin, “The Bernstein theorems for Fantappie indcatrix and their applications to mathematical economics,” Lect. Notes Pure Appl. Math. 132, 221–227 (1991).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia
  2. 2.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”Russian Academy of SciencesMoscowRussia
  3. 3.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia
  4. 4.Peoples Friendship UniversityMoscowRussia

Personalised recommendations