Estimation of Multiproduct Models in Economics on the Example of Production Sector of Russian Economy

  • Ivan Stankevich
  • Alexei UjegovEmail author
  • Sergey Vasilyev
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


The model of the real sector of the Russian economy is presented. It allows for the separate description of GDP and its components by expenditure both in constant and in current prices. Unlike standard macroeconomic models, the model proposed considers a set of Trader agents in addition to Producer agent. Traders are based on a set of CES-functions and allow to decompose the statistics available into a set of unobserved components. The Producer is based on a specific production function that performs well for Russian data and works with financial variables, such as credits and bank accounts. In contrary to the standard approach, the model is not linearized to get estimates of model parameters but is estimated directly using a set of nonlinear equations. The optimization is performed numerically and allows to get both series of unobserved model products and their prices and model parameters. The stability of the solution found is checked on simulated data.


Macroeconomic modeling Nonlinear models Gross Domestic Product (GDP) Mathematical programming 


  1. 1.
    An, S., Schorfheide, F.: Bayesian analysis of DSGE models. Econ. Rev. 26(2–4), 113–172 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Andreev, M., Pilnik, N., Pospelov, I.G., Vrzheshch, V.P., Masyutin, A.: Intertemporal three-product general equilibrium model of Russian economy. Int. J. Arts Sci. 6(1), 125–145 (2013)Google Scholar
  3. 3.
    Bilbiie, F.O., Ghironi, F., Melitz, M.J.: Endogenous entry, product variety, and business cycles. J. Polit. Econ. 120(2), 304–345 (2012)CrossRefGoogle Scholar
  4. 4.
    Birgin, E.G., Martinez, J.M., Raydan, M.: Algorithm 813: SPG-software for convex-constrained optimization. ACM Trans. Math. Softw. (TOMS) 27(3), 340–349 (2001)CrossRefGoogle Scholar
  5. 5.
    Chatterjee, S., Cooper, R.: Entry and exit, product variety and the business cycle (No. w4562). National Bureau of Economic Research (1993)Google Scholar
  6. 6.
    Christiano, L., Eichenbaum, M., Rebelo, S.: When Is the government spending multiplier large? J. Polit. Econ. 119, 78–121 (2011)CrossRefGoogle Scholar
  7. 7.
    Dixit, A.K., Stiglitz, J.E.: Monopolistic competition and optimum product diversity. Am. Econ. Rev. 67(3), 297–308 (1977)Google Scholar
  8. 8.
    Etro, F., Rossi, L.: New-Keynesian Phillips curve with Bertrand competition and endogenous entry. J. Econ. Dyn. Control 51, 318–340 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Guo, J.T., Krause, A.: Changing social preferences and optimal redistributive taxation. Oxford Econ. Pap. 70(1), 73–92 (2017)CrossRefGoogle Scholar
  10. 10.
    Hamano, M., Zanetti, F.: Endogenous product turnover and macroeconomic dynamics. Rev. Econ. Dyn. 26, 263–279 (2017)CrossRefGoogle Scholar
  11. 11.
    Minniti, A., Turino, F.: Multi-product firms and business cycle dynamics. Eur. Econ. Rev. 57, 75–97 (2013)CrossRefGoogle Scholar
  12. 12.
    Pilnik, N., Pospelov, I., Stankevich, I.: Multiproduct Model Decomposition of Components of Russian GDP. NRU Higher School of Economics. Series WP BRP “Economics/EC”. No. WP BRP 111/EC/2015 (2015)Google Scholar
  13. 13.
    Pilnik, N., Radionov, S.: On new approaches to the identification of blocks of general equilibrium models. Proc. MIPT 3(35), 151–161 (2017)Google Scholar
  14. 14.
    Smets, F., Wouters, R.: Shocks and frictions in US business cycles: a Bayesian DSGE approach. Am. Econ. Rev. 97(3), 586–606 (2007)CrossRefGoogle Scholar
  15. 15.
    Varadhan, R., Gilbert, P.: BB: an R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. J. Stat. softw. 32(4), 1–26 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Research University – Higher School of EconomicsMoscowRussia
  2. 2.The Lebedev Physical Institute of the Russian Academy of SciencesMoscowRussia
  3. 3.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia

Personalised recommendations