Granger Causal Linkages Between Economic Growth and Fixed Capital Formation in South Africa: A Frequency Domain Analysis

Abstract

The purpose of this study is to examine the Granger causal linkages between gross fixed capital formation (GFCF) growth and economic growth in South Africa. To provide a more comprehensive analysis of the Granger causality (GC) relationships between these macroeconomic indicators, this study investigates these causalities in the frequency domain. The methodology is based on decomposing time series into weighted sinusoidal components and performing separate GC tests for each component. Test results reveal that there is feedback between capital formation and economic growth in South Africa in the frequency domain, even at the 1% significance level. Furthermore, the test results indicate that the GC from fixed capital formation to economic growth is detected in lower frequencies compared to the GC from economic growth to capital formation. This means that the severity of the GC from economic growth to capital formation is stronger than the reverse direction GC in South Africa.

Keywords

• Frequency Domain Granger Causality
• Hodrick-Prescott Filter
• Bootstrap
• Economic Growth
• Capital Formation

Güney Afrika'da Ekonomik Büyüme ve Sabit Sermaye Oluşumu Arasındaki Granger Nedensel İlişkiler: Bir Frekans Alanı Analizi

Abstract

Bu çalışmanın amacı, Güney Afrika'da sabit sermaye oluşumu ile ekonomik büyüme arasındaki Granger nedensellik ilişkilerinin araştırılmasıdır. Bu makroekonomik göstergeler arasındaki Granger nedensel ilişkilerin daha kapsamlı bir analizini sağlamak için, nedensellikler frekans alanında araştırılmıştır. Yöntem, zaman serilerinin ağırlıklı sinüzoidal bileşenlerine ayrıştırılarak her bir bileşen için ayrı ayrı Granger nedensellik testinin gerçekleştirilmesine dayanmaktadır. Test sonuçları, Güney Afrika'da ekonomik büyüme ile sermaye oluşumu arasında, %1 önem düzeyinde dahi, frekans alanında çift yönlü bir Granger nedenselliğin olduğunu göstermektedir. Ayrıca, çalışma sabit sermaye oluşumundan ekonomik büyümeye olan Granger nedenselliğinin, ekonomik büyümeden sermaye oluşumuna olan Granger nedenselliğe kıyasla daha düşük frekanslarda mevcudiyet gösterdiğini de ortaya koymaktadır. Bu sonuçlar, Güney Afrika'da ekonomik büyümeden sermaye oluşumuna olan Granger nedenselliğin sermaye oluşumundan ekonomik büyümeye olan Granger nedensellikten daha güçlü olduğunu ifade etmektedir.

Keywords

• Frekans Alanında Granger Nedensellik
• Hodrick-Prescott Filtresi
• Bootstrap
• Ekonomik Büyüme
• Sermaye Oluşumu

References

1. Balcilar, M. (2019). _mFilter: Miscellaneous Time Series Filters_. R package version 0.1-5, .
2. Baxter, M., & King, R. G. (1999). Measuring business cycles: Approximate band-pass filters for economic time series. The Review of Economics and Statistics, 81(4), 575–593.
3. Breitung, J., & Candelon, B. (2006). Testing for short-and long-run causality: A frequency-domain approach. Journal of Econometrics, 132(2), 363-378.
4. Croux, C., & Reusens, P. (2013). Do stock prices contain predictive power for the future economic activity? A Granger causality analysis in the frequency domain. Journal of Macroeconomics, 35, 93-103.
5. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a), 427-431.
6. Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica: Journal of the Econometric Society, 49(4), 1057-1072.
7. Ding, M., Chen, Y., & Bressler, S. L. (2006). Granger causality: Basic theory and application to neuroscience. In B. Schelter, M. Winterhalder, & J. Timmer (Eds.) Handbook of time series analysis: Recent theoretical developments and applications, (pp. 437-460). Weinheim, Germany: WILEY-VCH Verlag GmbH & Co. KGaA.
8. Farnè, M., & Montanari, A. (2019). _grangers: Inference on Granger-Causality in the Frequency Domain_. R package version 0.1.0, .

9. Farnè, M., & Montanari, A. (2022). A bootstrap method to test Granger-causality in the frequency domain. Computational Economics, 59(3), 935-966.
10. Fuller, W. A. (1996). Introduction to statistical time series, Second Edition, John Wiley & Sons, Inc.
11. Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77(378), 304-313.
12. Granger, C. W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society, 37(3), 424-438.
13. Hodrick, R. J., & Prescott, E. C. (1997). Postwar US business cycles: An empirical investigation. Journal of Money, Credit, and Banking, 29(1).
14. International Monetary Fund. (2023). Regional economic outlook. Sub-Saharan Africa: The big funding squeeze. https://www.imf.org/en/Publications/REO/SSA/Issues/2023/04/14/regional-economic-outlook-for-sub-saharan-africa-april-2023.
15. Kesar, A., Bandi, K., Jena, P. K., & Yadav, M. P. (2023). Dynamics of governance, gross capital formation, and growth: Evidence from Brazil, Russia, India, China, and South Africa. Journal of Public Affairs, 23(1), e2831.
16. Kong, Y., Nketia, E. B., Antwi, S. K., & Musah, M. (2020). Scrutinizing the complex relationship between financial development gross fixed capital formation and economic growth in Africa by adopting CCEMG and AMG estimation techniques. International Journal of Science and Business, 4(11), 160-174.
17. Meyer, D., & Sanusi, K. (2019). A causality analysis of the relationships between gross fixed capital formation, economic growth and employment in South Africa. Studia Universitatis Babes-Bolyai Oeconomica, 64(1), 33-44.
18. Ncanywa, T., & Makhenyane, L. (2016). Can investment activities in the form of capital formation influence economic growth in South Africa?, SAAPAM Limpopo Chapter 5th. In Annual Conference Proceedings, 270-279.
19. Pasara, M. T., & Garidzirai, R. (2020). Causality effects among gross capital formation, unemployment and economic growth in South Africa. Economies, 8(2), 26.
20. Pfaff, B. (2008a). Analysis of integrated and cointegrated time series with R. Second Edition. New York: Springer. ISBN: 0-387-27960-1.
21. Pfaff, B. (2008b). VAR, SVAR and SVEC models: Implementation within R package vars. Journal of Statistical Software, 27(4).
22. Politis, D. N., & Romano, J. P. (1994). The stationary bootstrap. Journal of the American Statistical Association, 89(428), 1303-1313.
23. R Core Team (2023). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
24. Taraki, S. A., & Arslan, M. M. (2019). Capital formation and economic development. International Journal of Science and Research, 8(1), 772-780.
25. Trapletti, A., Hornik, K. (2023). _tseries: Time Series Analysis and Computational Finance_. R package version 0.10-54, .
26. Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54(3), 426-482.