Typology of macroeconomic disbalances in post-war recovery: justifying the number of clusters and the stability of the classification

Authors

DOI:

https://doi.org/10.26661/2522-1566/2026-3/37-11

Keywords:

macroeconomic disbalances, war period, post-war recovery, cluster analysis, silhouette coefficient, cophenetic correlation, classification validity, Ward’s method

Abstract

This article asks whether a cluster typology of post-war recovery trajectories is stable enough to carry the weight placed on it, and separates two claims such typologies conflate: that the episodes are heterogeneous, and that a given episode belongs to a given cluster. Design/methodology/approach. We cluster 50 recovery episodes, 18 of them post-conflict, described by nine disbalance indicators over a five-year stabilisation window, using Ward’s linkage on standardised annual World Bank series. The unit of observation is a country-window pair. Rather than reporting a single partition, we examine the silhouette profile across k from three to seven, the cophenetic correlation, and the agreement with a k-means solution. Findings. The silhouette coefficient rises from 0.134 at k = 3 to 0.196 at k = 6, then falls to 0.192 at k = 7, so six clusters is the last split that still improves separation. The cophenetic correlation is 0.735 and the agreement with k-means is 56 %; all three diagnostics are moderate, supporting the existence of structure but not the assignment of borderline episodes. An external check shows the partition does not reproduce shock type (adjusted Rand index 0.059), and post-conflict episodes differ from post-crisis ones on only two of the nine indicators, the trade balance and the current account. Originality/value. The contribution is a two-level reading of cluster validity, with a decision table linking each quality metric to the class of inference it supports, and a correction rule for transferring the benchmark profile to post-war Ukraine.

JEL Classification: C38, E32, O11, F44.

References

1. Булик О. Стратегія відновлення економіки України після війни. Економіка та суспільство. 2023. № 48. DOI: https://doi.org/10.32782/2524-0072/2023-48-51.

2. Caliński T., Harabasz J. A dendrite method for cluster analysis. Communications in Statistics. 1974. Vol. 3, no. 1. P. 1–27. DOI: https://doi.org/10.1080/03610927408827101.

3. Геєць В. М., Скрипниченко М. І., Шумська С. С. Макроекономічні дисбаланси в Україні: моніторинг на основі MIP Scoreboard та модельні оцінки їхнього впливу на зростання і стабільність. Фінансово-кредитна діяльність: проблеми теорії та практики. 2020. Т. 2, № 33. С. 296–305. DOI: https://doi.org/10.18371/fcaptp.v2i33.206956.

4. Gower J. C. A general coefficient of similarity and some of its properties. Biometrics. 1971. Vol. 27, no. 4. P. 857–871. DOI: https://doi.org/10.2307/2528823.

5. Milligan G. W., Cooper M. C. An examination of procedures for determining the number of clusters in a data set. Psychometrika. 1985. Vol. 50, no. 2. P. 159–179. DOI: https://doi.org/10.1007/BF02294245.

6. OECD. OECD Economic Surveys: Ukraine 2025. Paris : OECD Publishing, 2025. DOI: https://doi.org/10.1787/940cee85-en.

7. Rousseeuw P. J. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987. Vol. 20. P. 53–65. DOI: https://doi.org/10.1016/0377-0427(87)90125-7.

8. Rubin D. B. Inference and missing data. Biometrika. 1976. Vol. 63, no. 3. P. 581–592. DOI: https://doi.org/10.1093/biomet/63.3.581.

9. Скорик О. В. Аналітична інтерпретація кластерного аналізу зовнішньоекономічної діяльності та використання його результатів на мікро-рівні. Український економічний часопис. 2024. № 6. С. 137–141. DOI: https://doi.org/10.32782/2786-8273/2024-6-23.

10. Sokal R. R., Rohlf F. J. The comparison of dendrograms by objective methods. Taxon. 1962. Vol. 11, no. 2. P. 33–40. DOI: https://doi.org/10.2307/1217208.

11. Thorndike R. L. Who belongs in the family? Psychometrika. 1953. Vol. 18, no. 4. P. 267–276. DOI: https://doi.org/10.1007/BF02289263.

12. Tibshirani R., Walther G., Hastie T. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B. 2001. Vol. 63, no. 2. P. 411–423. DOI: https://doi.org/10.1111/1467-9868.00293.

13. Ward J. H., Jr. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association. 1963. Vol. 58, no. 301. P. 236–244. DOI: https://doi.org/10.1080/01621459.1963.10500845.

14. World Bank. Ukraine – Third Rapid Damage and Needs Assessment (RDNA3), February 2022 – December 2023. World Bank Group, 2024. URL: https://documents.worldbank.org/en/publication/documents-reports/documentdetail/099021324115085807 (дата звернення: 30.07.2026).

REFERENCES

Bulyk, O. (2023). Stratehiia vidnovlennia ekonomiky Ukrainy pislia viiny [Strategy for the recovery of Ukraine’s economy after the war]. Ekonomika ta suspilstvo, 48. https://doi.org/10.32782/2524-0072/2023-48-51 [in Ukrainian]

Caliński, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1–27. https://doi.org/10.1080/03610927408827101

Geyets, V. M., Skrypnychenko, M. I., & Shumska, S. S. (2020). Makroekonomichni dysbalansy v Ukraini: monitorynh na osnovi MIP Scoreboard ta modelni otsinky yikhnoho vplyvu na zrostannia i stabilnist [Macroeconomic disbalances in Ukraine: monitoring based on the MIP Scoreboard and model estimates of their impact on growth and stability]. Finansovo-kredytna diialnist: problemy teorii ta praktyky, 2(33), 296–305. https://doi.org/10.18371/fcaptp.v2i33.206956 [in Ukrainian]

Gower, J. C. (1971). A general coefficient of similarity and some of its properties. Biometrics, 27(4), 857–871. https://doi.org/10.2307/2528823

Milligan, G. W., & Cooper, M. C. (1985). An examination of procedures for determining the number of clusters in a data set. Psychometrika, 50(2), 159–179. https://doi.org/10.1007/BF02294245

OECD. (2025). OECD Economic Surveys: Ukraine 2025. OECD Publishing. https://doi.org/10.1787/940cee85-en

Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65. https://doi.org/10.1016/0377-0427(87)90125-7

Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592. https://doi.org/10.1093/biomet/63.3.581

Skoryk, O. V. (2024). Analitychna interpretatsiia klasternoho analizu zovnishnoekonomichnoi diialnosti ta vykorystannia yoho rezultativ na mikrorivni [Analytical interpretation of cluster analysis of foreign economic activity and the use of its results at the micro level]. Ukrainskyi ekonomichnyi chasopys, 6, 137–141. https://doi.org/10.32782/2786-8273/2024-6-23 [in Ukrainian]

Sokal, R. R., & Rohlf, F. J. (1962). The comparison of dendrograms by objective methods. Taxon, 11(2), 33–40. https://doi.org/10.2307/1217208

Thorndike, R. L. (1953). Who belongs in the family? Psychometrika, 18(4), 267–276. https://doi.org/10.1007/BF02289263

Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B, 63(2), 411–423. https://doi.org/10.1111/1467-9868.00293

Ward, J. H., Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236–244. https://doi.org/10.1080/01621459.1963.10500845

World Bank. (2024). Ukraine – Third Rapid Damage and Needs Assessment (RDNA3), February 2022 – December 2023. World Bank Group. https://documents.worldbank.org/en/publication/documents-reports/documentdetail/099021324115085807

Published

2026-10-19

Issue

Section

Economics and international economic relations

How to Cite

Khrushch, Y. (2026) “Typology of macroeconomic disbalances in post-war recovery: justifying the number of clusters and the stability of the classification”, Management and Entrepreneurship: Trends of Development, 3(37), pp. 151–167. doi:10.26661/2522-1566/2026-3/37-11.