Method for Correcting Panel Data Heterogeneity in the Models of Complex Economic Systems

The article is devoted to the construction of models for panel data that take into account the influence of qualitative features on the endogenous variable. Dummy variables are an econometric tool that formalizes the influence of qualitative features. The need to include dummy variables in econometric models was recently dictated by structural changes in the economies of a number of countries caused by unprecedented Western sanctions and changes associated with the pandemic. The aim of this study is to develop and empirically test a model of Russia’s trade turnover with BRICS countries using panel data techniques that account for the impact of qualitative (time-invariant) factors on the endogenous variable, employing Fixed effects vector decomposition (FEVD) method. FEVD approach provides a more flexible model specification by combining the advantages of fixed and random effects models without relying on the strict assumption of zero correlation between individual effects and regressors, which is typical of random effects models. This enhances the capabilities of panel data analysis in econometrics and enables more accurate modeling of the influence of qualitative factors on the endogenous variable. The objectives of the study include: building models for panel data based on BRICS data, conducting their specification tests, implementing FEVD method algorithm in the R software environment, and algebraic and empirical verification of the properties of the method parameter estimates. The result of the work is adaptation of FEVD method to the specifics of BRICS economies in the context of modern economic challenges. Balanced panel data for five BRICS countries (Brazil, Russia, India, China, South Africa) for the period 2000–2020 were used as an empirical base. Particular attention is paid to the analysis of the impact of macroeconomic indicators (GDP, dollar exchange rate, oil price, pandemic shock, etc.) on Russia’s trade turnover with BRICS countries. The FEVD method made it possible to increase the accuracy of the estimation results in comparison with the traditional fixed effects model. The study contributes to the empirical base for estimating fixed effects models using FEVD method.

1. Abakumova Ju.G., Pavlovskaja S. V. (2010). Matrix modeling of bilateral trade relations of countries. Vectors of foreign economic activity. Ed. by V. M. Rudenkov et al. Minsk: Institute of Economics of the National Academy of Sciences of Belarus. P. 71–382. (In Russ.)

2. Babeshko L. O., Byvshev V. A. (2025). Analysis of the stability of the model for forecasting mutual volumes Russia’s trade with BRICS partners. Finance: Theory and Practice, vol. 29, no. 4, pp. 129–145. (In Russ.) DOI: 10.26794/2587-5671-2025-29-4-1902-01

3. Babeshko L. O., Mikhaleva M.Yu. (2025). Quantitative assessment of the impact of the volume of loans issued on the profit level of commercial banks in Russia. Fundamental Research, no. 2, pp. 23–35. (In Russ.)

4. Babeshko L. O., Kharitonov D. A. (2024) Checking the adequacy of the turnover model Russia and China by the Salkever method. Soft measurements and computing, vol. 84, no. 11, pp. 103–111. (In Russ.) DOI: 10.36871/2618-9976.2024.11.008

5. Balyhin M. G., Shajlieva M. M., Tsypin A. P. Statistical Analysis of the Economic Development of the BRICS Countries // Statistics and Economics, no. 17 (2), pp. 18–28. (In Russ.)

6. Byvshev V. A. (2022). Forecasting mutual trade volumes between countries based on macroeconomic indicators. Research report within the framework of the Temporary Creative Student Team (VTSK). No. 17. (In Russ.)

7. Kartayev F. S. (2019). Introduction to Econometrics: Textbook. Moscow: Moscow State University. 472 p. (In Russ.)

8. Radionova M. V., Kulakova A. M. Modeling of mutual commodity trade between countries (a case study of the Eurasian economic union member states per industry). Financial Analytics: Science and experience, no. 34, pp. 41–54. (In Russ.)

9. Econometrics (2025). Econometrics: Textbook for Universities. Ed. by I. I. Eliseeva. Moscow: Yurayt. 449 p. (In Russ.)

10. Abdixhiku L., Pugh G., Hashi I. (2018). Business Tax Evasion in Transition Economies: A Cross-Country Panel Investigation. The European Journal of Comparative Economics, vol. 15 (1), pp. 11–36.

11. Breusch T., Ward M. B., Nguyen H. T.M., Kompas T. (2011). On the Fixed-Effects Vector Decomposition. Political Analysis, vol. 19 (2), pp. 123–134.

12. Chatelain J.-B., Ralf K. (2021).Inference on time-invariant variables using panel data: A pretest estimator // HAL+SHS Id: Halshs‑01719835. URL: https://shs.hal.science/halshs‑01719835v2

13. Chaudhry A., Hyder K. (2012). A Structural VAR Analysis of Pakistan’s Textile Export. Middle-East Journal of Scientific Research, vol. 12 (4), pp. 464–478.

14. Chen H. (2009). The analysis of simultaneous multi equations model on the relationship between trade and economic growth in China. International Journal of Business and Management, vol. 4 (1), pp. 162–166. DOI: https://doi.org/10.5539/ijbm.v4n1p162.

15. Greene W. (2011). Fixed Effects Vector Decomposition: A Magical Solution to the Problem of Time Invariant Variables in Fixed Effects Models. Political Analysis, vol. 19, pp. 135–146.

16. Hausman J. A., Taylor W. E. (1981). Panel data and unobservable individual effects. Econometrica, vol. 49, pp. 1377–1398.

17. Kleiber C., Zeileis A. (2008). Applied Econometrics with R. New York: Springer. 232 p.

18. Plümper T., Troeger V. (2007). Efficient Estimation of Time Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects. Political Analysis, vol. 15, pp. 124–139.

19. Plümper T., Troeger V. (2011). Fixed-Effects Vector Decomposition: Properties, Reliability, and Instruments. Political Analysis, vol. 19 (2), pp. 147–164. URL: http://www.jstor.org/stable/23011259

20. Sellner R. (2019). Non-discriminatory Trade Policies in Panel Structural Gravity Models: Evidence from Monte Carlo Simulations. Review of International Economics, vol. 27 (3), pp. 854–887.

21. World Bank. (2020). World Development Report 2020: Trading for Development in the Age of Global Value Chains. Washington (DC): World Bank.