Hierarchical Bayesian Modelling of Macroeconomic Variables in Ghana
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Emmanuel Amoako Koranteng
,
Gideon Mensah Engmann
Abstract
This study analyzed the impact of macroeconomic variables (manufacturing, real exchange rate, government expenditure, and gross fixed capital formation) on GDP growth in Ghana. Utilizing secondary data from the World Development Indicators of the World Bank (1991–2021), we employed a hierarchical Bayesian linear model with interaction effects to assess these relationships. The results indicate that the real exchange rate, manufacturing, and government expenditure have a positive influence on GDP growth, while gross fixed capital formation exhibits a moderately negative effect. To enhance economic growth, it is crucial to optimize capital investments, bolster export competitiveness through targeted policies, and invest in manufacturing innovation. These findings offer actionable insights for policymakers aiming to stimulate economic growth in Ghana.
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Author contributions: Conceptualization: Emmanuel Amoako Koranteng, Gideon Mensah Engmann, Jakperik Dioggban. Data curation: Emmanuel Amoako Koranteng. Formal analysis: Emmanuel Amoako Koranteng. Investigation: Emmanuel Amoako Koranteng. Methodology: Emmanuel Amoako Koranteng. Project administration: Emmanuel Amoako Koranteng, Gideon Mensah Engmann, Jakperik Dioggban. Resources: Emmanuel Amoako Koranteng. Software: Emmanuel Amoako Koranteng. Supervision: Gideon Mensah Engmann, Jakperik Dioggban. Validation: Emmanuel Amoako Koranteng. Visualization: Emmanuel Amoako Koranteng. Writing – original draft: Emmanuel Amoako Koranteng. Writing – review & editing: Emmanuel Amoako Koranteng, Gideon Mensah Engmann, Jakperik Dioggban.
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Conflict of interest: There are no reported conflict of interest by the author(s).
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Research funding: No funding for this study.
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Data availability: The data used to support the findings of this study are available from (https://databank.worldbank.org/source/world-development-indicators).
APPENDIX A: Model Selection
Information Criteria.
| Models | DIC | WAIC | LOOIC |
|---|---|---|---|
| Linear model | 5.710 | −670.605 | 775.6 |
| Linear model (Interaction) | 5.413 | −632.572 | 634.9 |
| Nonlinear model | 5.684 | −665.459 | 3,131.4 |
| Nonlinear model (Interaction) | 5.640 | −663.964 | 3,997.4 |
-
The least values used in the selection of the model, where the linear model with interaction had two of them for it to be selected as the best model are given in bold.
Estimated expected log pointwise predictive Density.
| Models | ELPD_LOO |
|---|---|
| Linear model | −387.8 |
| Linear model (Interaction) | −317.5 |
| Nonlinear model | −1,565.7 |
| Nonlinear model (Interaction) | −1,998.7 |
-
The least values used in the selection of the model, where the linear model with interaction had two of them for it to be selected as the best model given in bold.
Gelmans diagnostic for the linear model.
| Potential scale-reduction factors | ||
|---|---|---|
| Point est. | Upper C.I. | |
|
|
||
| Intercept | 1 | 1 |
| Exchange rate | 1 | 1 |
| Gross fixed capital formation | 1 | 1 |
| Manufacturing | 1 | 1 |
| Government exp. | 1 | 1 |
| Log of time | 1 | 1 |
| Error term | 1 | 1 |
| Multivariate potential scale-reduction factors: | 1 | |
Gelmans diagnostic for the linear model with interactive Effect.
| Potential scale-reduction factors | ||
|---|---|---|
| Point est. | Upper C.I. | |
|
|
||
| b0 | 1 | 1 |
| b1 | 1 | 1 |
| b2 | 1 | 1 |
| b3 | 1 | 1 |
| b4 | 1 | 1 |
| b5 | 1 | 1 |
| d1 | 1 | 1 |
| d2 | 1 | 1 |
| d3 | 1 | 1 |
| d4 | 1 | 1 |
| d5 | 1 | 1 |
| d6 | 1 | 1 |
| Tau | 1 | 1 |
| Multivariate potential scale reduction factor: | 1 | |
Gelmans diagnostic for the rational (total) nonlinear Model.
| Potential scale-reduction factors | ||
|---|---|---|
| Point est. | Upper C.I. | |
|
|
||
| A | 1 | 1 |
| b1 | 1 | 1 |
| b2 | 1 | 1 |
| b3 | 1 | 1 |
| b4 | 1 | 1 |
| b5 | 1 | 1 |
| c1 | 1 | 1 |
| c2 | 1 | 1 |
| c3 | 1 | 1 |
| c4 | 1 | 1 |
| c5 | 1 | 1 |
| Tau | 1 | 1 |
| Multivariate potential scale reduction factor: | 1 | |
Gelmans diagnostic for the rational (total) nonlinear model with interaction.
| Potential scale-reduction factors | ||
|---|---|---|
| Point est. | Upper C.I. | |
|
|
||
| A | 1 | 1 |
| b1 | 1 | 1 |
| b2 | 1 | 1 |
| b3 | 1 | 1 |
| b4 | 1 | 1 |
| b5 | 1 | 1 |
| c1 | 1 | 1 |
| c2 | 1 | 1 |
| c3 | 1 | 1 |
| c4 | 1 | 1 |
| c5 | 1 | 1 |
| d1 | 1 | 1 |
| d2 | 1 | 1 |
| d3 | 1 | 1 |
| d4 | 1 | 1 |
| d5 | 1 | 1 |
| d6 | 1 | 1 |
| Tau | 1 | 1 |
| Multivariate potential scale reduction factor: | 1 | |
APPENDIX B: Model Diagnostics
Hierarchical Bayesian Linear Model
Trace Plots for the Linear Model (Figures 1–8)
Trace plots of posterior parameters of the linear model.
Autocorrelation plots of posterior parameters of the linear Model.
Trace plots of posterior parameters of the linear model (Interactions).
Autocorrelation plots of posterior parameters of the linear model with interactions.
Trace plots of posterior parameters of the nonlinear Model.
Autocorrelation plots of posterior parameters of the rational nonlinear model.
Trace plots of posterior parameters of the nonlinear model (Interaction).
Autocorrelation plots of posterior parameters of the rational nonlinear model (Interaction).
Gelmans Diagnostic for the Linear Model
Autocorrelation Plots of Posterior Parameters of the Linear Model
Hierarchical Bayesian Linear Model with Interactive Effect
Trace Plots for the Linear Model with Interactive Effect
Gelmans Diagnostic for the Linear Model with Interactive Effect
Autocorrelation Plots of Posterior Parameters of the Linear Model with Interactions
Hierarchical Bayesian Rational (total) Nonlinear Model
Trace Plots for the Rational (total) Nonlinear Model
Gelmans Diagnostic for the Rational (total) Nonlinear Model
Autocorrelation Plots of Posterior Parameters of the Rational (total) Nonlinear Model
Hierarchical Bayesian Rational (total) Nonlinear Model with Interactions
Trace Plots for the Rational (total) Nonlinear Model with Interactions
Gelmans Diagnostic for the Rational (total) Nonlinear Model with Interactions
Autocorrelation Plots of Posterior Parameters of for the Rational (total) Nonlinear Model with Interactions
APPENDIX C: Prior Distributions and Resulting Posterior Distributions
Linear model with interactive effect.
| Prior | Mean | SD | 2.5 % | 50 % | 97.5 % | R-hat | n.eff | |
|---|---|---|---|---|---|---|---|---|
| INTERCEPT | N (0,0.001) | −22.00 | 9.600 | −40.00 | −22.00 | −2.800 | 1 | 12,621 |
| RER | N (0,0.001) | 12.00 | 4.600 | 2.800 | 12.000 | 21.000 | 1 | 23,714 |
| GFCF | N (0,0.001) | −0.81 | 0.660 | −2.100 | −0.810 | 0.480 | 1 | 13,644 |
| MA | N (0,0.001) | 2.500 | 1.200 | 0.160 | 2.5000 | 4.700 | 1 | 15,211 |
| GOVEXP | N (0,0.001) | 3.300 | 1.100 | 1.000 | 3.3000 | 5.500 | 1 | 12,319 |
| RER*GFCF | N (0,0.001) | −0.099 | 0.120 | −0.330 | −0.0990 | 0.130 | 1 | 44,162 |
| RER*MA | N (0,0.001) | −0.940 | 0.360 | −1.700 | −0.9400 | −0.230 | 1 | 30,041 |
| GFCF*GOVEXP | N (0,0.001) | −0.0030 | 0.039 | −0.080 | −0.0030 | 0.074 | 1 | 22,332 |
| MA*GOVEXP | N (0,0.001) | −0.3400 | 0.093 | −0.520 | −0.3400 | −0.150 | 1 | 12,902 |
| RER*GOVEXP | N (0,0.001) | −0.0042 | 0.240 | −0.480 | −0.0048 | 0.470 | 1 | 62,779 |
| GFCF*MA | N (0,0.001) | 0.0930 | 0.068 | −0.040 | 0.0930 | 0.230 | 1 | 12,625 |
| SIGMA | Inverse-gamma (2,1) | 0.0830 | 0.016 | 0.054 | 0.0820 | 0.120 | 1 | 77,654 |
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Articles
- Party Proximities in Voting Advice Applications – Identifying Structural Breaks in Data from the German Wahl-O-Mat
- A Geometric Model of Elections in Five Federal Democracies
- Hybrid Modeling Techniques for Municipal Solid Waste Forecasting: An Application to OECD Countries
- The Great Powers Competition and Increasing Entropy in the Local Media Across Africa and Asia
- Hierarchical Bayesian Modelling of Macroeconomic Variables in Ghana
Articles in the same Issue
- Frontmatter
- Articles
- Party Proximities in Voting Advice Applications – Identifying Structural Breaks in Data from the German Wahl-O-Mat
- A Geometric Model of Elections in Five Federal Democracies
- Hybrid Modeling Techniques for Municipal Solid Waste Forecasting: An Application to OECD Countries
- The Great Powers Competition and Increasing Entropy in the Local Media Across Africa and Asia
- Hierarchical Bayesian Modelling of Macroeconomic Variables in Ghana
