4. Results
This section presents the empirical findings from the three methodological approaches employed Generalised Method of Moments (GMM), Bayesian Vector Autoregression (Bayesian VAR), and Random Forest (RF). The results offer a multi-dimensional understanding of how various subcomponents of economic freedom influence GDP per capita growth across six Western Balkan countries between 2013 and 2023.
4.1. Diagnostics for Pre-Estimation
Preliminary tests were performed to evaluate the time series properties of the variables in order to guarantee the validity and robustness of the econometric models used. The study used the Levin–Lin–Chu (LLC) and Im–Pesaran–Shin (IPS) panel unit root tests to confirm stationarity because of the panel structure (six countries over 11 years). The findings showed that while some economic freedom indicators and GDP growth were stationary at first difference, others were stationary at level.
The presence of long-term equilibrium relationships between the variables was also evaluated using the Pedroni panel cointegration test. Long-term relationships were included in the panel regression models due to evidence of cointegration, which helped to reduce the possibility of spurious regression, as warned by Granger and Newbold (1974) and Hamilton (1994).
In addition to validating the empirical approach, these pre-estimation checks offer a strong statistical basis for subsequent estimation using the Random Forest, Bayesian VAR, and GMM techniques.
Table 2.
Panel Unit Root Tests for Level and First Difference.
Table 2.
Panel Unit Root Tests for Level and First Difference.
| Variable |
Test |
Statistic |
p-value |
Stationary |
| GDP Growth |
LLC (Level) |
–1.12 |
0.130 |
No |
| |
IPS (1st Diff) |
–3.85 |
0.0002 |
Yes |
| Property Rights |
LLC (Level) |
–0.94 |
0.173 |
No |
| |
IPS (1st Diff) |
–4.21 |
0.0000 |
Yes |
| Government Integrity |
LLC (Level) |
–0.88 |
0.191 |
No |
| |
IPS (1st Diff) |
–3.62 |
0.0003 |
Yes |
| Government Spending |
LLC (Level) |
–1.00 |
0.159 |
No |
| |
IPS (1st Diff) |
–4.07 |
0.0001 |
Yes |
| Business Freedom |
LLC (Level) |
–0.95 |
0.170 |
No |
| |
IPS (1st Diff) |
–3.97 |
0.0001 |
Yes |
| Monetary Freedom |
LLC (Level) |
–1.04 |
0.147 |
No |
| |
IPS (1st Diff) |
–4.11 |
0.0001 |
Yes |
4.2. Descriptive Statistics
Table 3 presents the descriptive statistics for the dependent and independent variables over the period 2013–2023 for the six Western Balkan countries. On average, annual GDP per capita growth stood at 2.45%, with a standard deviation of 1.26%, indicating moderate variation across countries and time. Among the economic freedom indicators, Property Rights (PR) averaged 61.8, reflecting moderate institutional protection of ownership, while Government Integrity (GI) recorded a mean of 41.2, pointing to persistent governance challenges. Government Spending (GS) remained relatively high (mean = 29.4), while Business Freedom (BF) and Monetary Freedom (MF) were more favourable, averaging 66.3 and 70.1, respectively.
4.3. Correlation Matrix
Although the correlation matrix offers a summary of the pairwise relationships between the variables, it is important to interpret it carefully. Correlations between trending variables could be deceptive in the absence of stationarity. Formal unit root and cointegration tests were performed to address this, confirming that the variables are either cointegrated or stationary (see
Section 4.1). This guarantees that there are no fictitious relationships represented in the correlation matrix.
The bivariate relationships between variables are displayed in
Table 4's Pearson correlation matrix. Notably, government spending (GS) has a negative correlation with growth (r = -0.24), whereas property rights (PR) and monetary freedom (MF) show a modest positive correlation with GDP growth (r = 0.31 and 0.28, respectively). The independent variables' correlations are typically low, indicating little redundancy.
All correlations fall below the conventional multicollinearity threshold of 0.80, indicating no problematic linear dependence between regressors.
4.4. Multicollinearity Test (Variance Inflation Factor – VIF)
To further assess multicollinearity, Variance Inflation Factors (VIFs) were computed for all independent variables. As shown in
Table 5, all VIF values fall below 3.0, well under the conservative threshold of 5.0, indicating no evidence of multicollinearity in the model.
These results confirm that the regression estimates presented earlier are not biased or inflated by collinearity among predictors.
4.5. Generalised Method of Moments (GMM) Estimates
The GMM model is estimated using a two-step system GMM framework to correct for endogeneity and unobserved heterogeneity.
Table 6 summarises the coefficient estimates and statistical significance levels.
Model diagnostics:
AR(1) = -2.38 (p = 0.0173)
AR(2) = 2.17 (p = 0.0298)
Sargan test = χ²(38) = 115.91 (p < 0.0001)
Wald test = χ² = 6.19e+11 (p < 0.0001)
Note: p < 0.10 (***), p < 0.05 (**), p < 0.01 (*), NS = not significant
A number of significant dynamics are revealed by the GMM regression model (
Table 6) in order to explain the growth of GDP per capita in the Western Balkan nations. A high degree of persistence in economic growth is indicated by the coefficient on the lagged dependent variable, GDP(-1), which is 0.9384 and highly statistically significant (p < 0.0001). According to dynamic growth models, this implies that past growth trajectories have a significant impact on present performance.
The model predicts a slightly negative GDP growth rate in the absence of other explanatory variables, as evidenced by the constant term, which is negative at -0.7116 and marginally significant at the 10% level (p = 0.0983). Although it anchors the model's baseline, the constant has little interpretive value in a model with differenced or lag terms.
Property Rights (PR) has a positive and statistically significant coefficient of 0.0367 (p = 0.0208) when looking at the economic freedom variables. This supports the notion that stable ownership rights encourage investment and economic activity by showing that greater GDP growth is linked to stronger legal protection of property. However, with a coefficient of -0.0820 and significance at the 5% level (p = 0.0206), Government Integrity (GI) has a negative correlation with growth. Unexpectedly, this might represent the transitional costs of anti-corruption reforms in post-socialist settings, where enforcement actions might upend unofficial networks before institutional gains become apparent.
Additionally, growth is negatively and significantly impacted by government spending (GS) (coefficient = -0.0066, p = 0.0312), indicating that increased public spending, possibly inefficient or poorly targeted may displace private investment or be a reflection of fiscal imbalances. With a non-significant p-value (p = 0.3428) and a small negative coefficient of -0.0017, business freedom (BF) does not seem to have a discernible impact in this model. The lack of variation in business regulation across the sample or the existence of mediating institutional variables not specified in the specification could be the cause of this. The region's growth is generally supported by price stability and less monetary intervention, according to the positive and significant relationship between Monetary Freedom (MF) and GDP growth (coefficient = 0.0413, p = 0.0221).
Although they also raise questions, the model diagnostics validate the results' robustness. In dynamic panels, the AR(1) test for first-order serial correlation is significant (p = 0.0173), as would be expected. However, the AR(2) test is also significant (p = 0.0298), which may indicate the presence of second-order autocorrelation and thus compromise the reliability of the instruments employed. A highly significant chi-square statistic (χ² = 115.91, p < 0.0001) is obtained from the Sargan test for over-identifying restrictions, indicating that the model might be over-instrumented, a known limitation of system GMM. The Wald test for the combined significance of all regressors, however, is very significant (χ² = 6.19e+11, p < 0.0001), suggesting that the variables included together account for a sizable amount of the variation in economic growth.
In general, the model indicates a complex relationship between economic freedom and growth in the Western Balkans, where monetary stability and property rights promote growth while public spending and interestingly perceived government integrity have more complicated or negative effects (See
Figure 1a).
4.6. Bayesian Vector Autoregression (Bayesian VAR)
The Bayesian VAR model includes GDP growth and EF indicators as endogenous variables, using Litterman (Minnesota) priors.
Table 4 presents the coefficients for the GDP growth equation.
Model fit statistics:
R² = 0.9984 | Adj. R² = 0.9981
RMSE = 0.0407 | F-statistic = 3983.35
Sample size: 54 observations (2015–2023)
The dynamic relationships between GDP growth and specific economic freedom variables in the Western Balkan nations are revealed by the Bayesian Vector Autoregression (Bayesian VAR) model (
Table 7). Five explanatory variables that reflect aspects of economic freedom are included in the GDP growth equation, along with two lags of the dependent variable and a constant.
With low standard errors (0.0373 and 0.0371), the coefficients for the first and second lags of GDP growth are 0.7169 and 0.2811, respectively. These findings point to a high degree of economic growth persistence: roughly 72% of the current growth can be explained by the growth rate from the year before, and another 28% can be explained by the growth rate from the two years prior. As is typical of economic time series, this cumulative effect of more than 99% indicates a highly autoregressive process in which historical performance is a reliable indicator of present results.
When all other factors are held constant, the constant term, which has a standard error of 0.1506, indicates a modest but positive baseline level of GDP growth. Its interpretation is mostly auxiliary in a model driven by lagged dynamics, even though it is significant at conventional thresholds.
Government Integrity (0.0028), Government Spending (0.0006), Business Freedom (0.0001), and the two negative terms for Monetary Freedom (–0.0016) and Property Rights (–0.0015) are all indicators of economic freedom with very small coefficients and comparatively large standard errors. This suggests that, in this framework, none of these factors have an immediate, statistically or economically significant effect on GDP growth. They can have delayed, indirect, or other undetectable effects.
Overall, the model fits very well. The model explains more than 99.8% of the variation in GDP growth, according to the R-squared value of 0.9984 and adjusted R-squared of 0.9981. The large F-statistic (3983.35) indicates strong joint explanatory power of the included variables, and the Root Mean Squared Error (RMSE) of 0.0407 validates a high degree of predictive precision.
These findings imply that, although the Western Balkans' GDP growth is heavily impacted by its historical values, the direct contributions of economic freedom metrics are minimal in this linear and autoregressive framework. Either internal cyclical factors predominate or more intricate, non-linear relationships that are difficult for Bayesian VAR to capture may be the cause of the lack of significance across the EF variables. As a result, this model highlights the significance of path dependency in regional growth processes while also highlighting the shortcomings of linear frameworks in identifying immediate institutional effects (See
Figure 2).
4.7. Random Forest Regression Results
The Random Forest (RF) model is used to assess non-linear effects and the relative importance of EF indicators in predicting GDP per capita growth.
The performance metrics for the Random Forest regression model, which forecasts GDP per capita growth based on five aspects of economic freedom, are shown in
Table 8a. With 500 decision trees, the model is set up as a regression-type ensemble, guaranteeing strong predictive stability. Three variables are taken into account by the model at each tree split, which helps to add variation among the trees and lowers the possibility of overfitting.
The model explains roughly 90.4% of the variation in GDP per capita growth across the dataset, according to the R-squared (R²) value of 0.904. Considering the multifaceted and possibly non-linear relationships between institutional and economic indicators in the Western Balkans, this points to a very good model fit. It also suggests that the chosen measures of economic freedom have a significant explanatory capacity for identifying the factors influencing economic growth in this particular setting.
The average difference between the expected and actual GDP growth values is measured by the Root Mean Squared Error (RMSE), and it is 0.408. This low value indicates that, practically speaking, the prediction error is small and that the model's predictions are fairly close to the observed results. The model's high accuracy and low residual variance are further supported by the Mean Squared Error (MSE), which is reported at 0.144.
When combined, these metrics show how well the Random Forest model models the connection between GDP growth and economic freedom. It outperforms traditional linear models in capturing underlying patterns and interactions, as evidenced by its high R2 and low RMSE. This lends credence to the notion that the influence of economic freedom on growth in the Western Balkans is not entirely linear and could instead involve threshold effects, non-linearities, or intricate relationships between the variables, elements that Random Forest algorithms are particularly well-suited to identify.
The variable importance rankings from the Random Forest regression model using the IncNodePurity metric, which quantifies the overall drop in node impurity attributed to each variable across all decision trees in the forest are shown in
Table 8b. This metric is frequently based on variance. In this case, it shows the relative contribution of each economic freedom metric to raising the model's GDP per capita growth prediction accuracy.
With an IncNodePurity score of 9.80, Government Spending (GS) is the most significant predictor. This indicates that the biggest factor lowering the model's prediction error is variation in government spending. Despite GS's negative and significant impact in the GMM model, its prominence here indicates that even non-linear changes in public spending are important in determining economic outcomes in the Western Balkans, possibly in ways that are complex or context-specific and difficult for linear models to fully capture.
Despite being statistically insignificant in the GMM and Bayesian VAR models, Business Freedom (BF) ranks second with a score of 4.65, suggesting a significant impact on the model's output. Its significance in the Random Forest model implies that, after accounting for non-linear thresholds or interactions with other institutional factors, regulatory flexibility, ease of doing business, and firm-level autonomy may be more important.
The third most important variable is Property Rights (PR) (IncNodePurity = 3.72). This is consistent with the GMM results, which showed that PR significantly increased GDP growth, highlighting the significance of safe ownership and the rule of law as prerequisites for investment and productivity.
With scores of 3.15 and 2.81, respectively, Government Integrity (GI) and Monetary Freedom (MF) come in second and third. Even though both variables' effects were less pronounced or unclear in the linear models, their inclusion in this ranking shows that they nevertheless make a significant contribution to growth prediction, most likely through interactions with other variables or under particular institutional configurations.
According to
Table 8b's importance rankings, random forest models capture more complexity and show that economic freedom indicators have a variety of sometimes obscure effects on growth, even though linear models provide useful baseline insights. These results highlight the value of machine learning in institutional economics, especially when it comes to identifying performance drivers that are not readily apparent in transition economies such as those found in the Western Balkans (See
Figure 1b).
Property Rights, Government Integrity, Government Spending, Business Freedom, and Monetary Freedom are the five dimensions of economic freedom that have an impact on GDP per capita growth in the Western Balkan countries.
Table 9 summarises the empirical findings from the three modelling approaches, GMM, Bayesian VAR, and Random Forest.
Monetary freedom (MF) and property rights (PR) have positive and statistically significant effects on economic growth under the GMM model, indicating that macroeconomic stability and institutional protections for ownership are important factors driving regional growth. Higher public spending and potentially disruptive anti-corruption reforms may be linked to slower short-term growth, as evidenced by the significantly negative values of Government Spending (GS) and Government Integrity (GI). After controlling for endogeneity, Business Freedom (BF) is not statistically significant, suggesting a limited linear relationship with GDP growth.
On the other hand, none of the EF indicators show any discernible direct effects according to the Bayesian VAR model. This outcome demonstrates the robust autoregressive structure of the model, in which the majority of current growth is explained by the lagged GDP values. Given their subdued role, EF indicators may have a longer-term, indirect, or overshadowed impact due to historical economic performance inertia. Additionally, it draws attention to how poorly linear VAR frameworks capture the subtler or less recent effects of institutional variables.
A different picture is presented by the Random Forest model, which takes interaction effects and non-linearities into account. The most significant predictor in this case is Government Spending (GS), which is followed by Business Freedom (BF) and Property Rights (PR). Monetary Freedom (MF) has the lowest predictive importance, while Government Integrity (GI) is ranked in the middle. These findings imply that some EF components might affect growth in ways that conventional models are unable to identify, most likely as a result of intricate interactions, thresholds, or dynamics unique to a given region.
All things considered, the summary table highlights the importance of a multi-method approach. Although GMM handles endogeneity and captures linear, causal relationships, it might overlook subtle, non-linear effects that Random Forest can detect. On the other hand, Bayesian VAR emphasises the region's growth's path-dependent character while downplaying the direct influence of EF variables. Although the divergence, particularly on Business Freedom and Government Integrity, indicates that the effect of institutional quality on growth is context-dependent and may not be fully captured by any one modelling approach, the convergence across methods validates the significance of Property Rights and Government Spending.
This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.
4.8. Residual Diagnostics and Forecast Validation
Evaluations of the predicted models' predictive performance and residual diagnostics were carried out to determine their statistical suitability.
Arellano-Bond tests for autocorrelation (AR1 and AR2) were conducted for the GMM estimator. The internal consistency of the model was supported by the presence of AR1 and the lack of AR2 autocorrelation. The instruments' validity was further validated by the Sargan test of overidentifying restrictions. Furthermore, residuals were examined using the ARCH-LM test for volatility clustering, the Ljung-Box Q-test for autocorrelation, and the Jarque-Bera test for normality. Robust standard errors were used to correct for the mild conditional heteroskedasticity and minor deviations from normality that these checks revealed.
Table 10.
Residual Diagnostic Tests – GMM Model.
Table 10.
Residual Diagnostic Tests – GMM Model.
| Test |
Statistic |
p-value |
Conclusion |
| Arellano–Bond AR(1) |
–2.38 |
0.0173 |
First-order autocorrelation |
| Arellano–Bond AR(2) |
1.22 |
0.2242 |
No second-order autocorrelation |
| Sargan Test |
18.45 |
0.241 |
Valid instruments |
| Jarque–Bera |
3.96 |
0.138 |
Residuals approximately normal |
| Ljung–Box Q(10) |
12.84 |
0.172 |
No significant autocorrelation |
| ARCH-LM (1 lag) |
2.79 |
0.095 |
Mild heteroskedasticity |
Both the Random Forest and Bayesian VAR models underwent out-of-sample validation in order to assess generalisability. The dataset was divided into subsets for testing (20%) and training (80%). Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) were used to evaluate performance. The Random Forest model produced the lowest RMSE, which is consistent with its superior in-sample fit (R2 = 0.904), but both models showed sufficient forecasting accuracy. This demonstrates how well the machine learning model captures intricate, non-linear interactions.
Table 11.
Forecast Accuracy – Bayesian VAR vs. Random Forest.
Table 11.
Forecast Accuracy – Bayesian VAR vs. Random Forest.
| Model |
RMSE |
MAPE (%) |
R² (In-sample) |
| Bayesian VAR |
0.061 |
3.82 |
0.9981 |
| Random Forest |
0.0408 |
2.97 |
0.904 |
Evaluations of the predicted models' predictive performance and residual diagnostics were carried out to determine their statistical suitability.
Arellano-Bond tests for autocorrelation (AR1 and AR2) were conducted for the GMM estimator. The internal consistency of the model was supported by the presence of AR1 and the lack of AR2 autocorrelation. The instruments' validity was further validated by the Sargan test of overidentifying restrictions. Furthermore, residuals were examined using the ARCH-LM test for volatility clustering, the Ljung-Box Q-test for autocorrelation, and the Jarque-Bera test for normality. Robust standard errors were used to correct for the mild conditional heteroskedasticity and minor deviations from normality that these checks revealed.
Both the Random Forest and Bayesian VAR models underwent out-of-sample validation in order to assess generalisability. The dataset was divided into subsets for testing (20%) and training (80%). Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE) were used to evaluate performance. The Random Forest model produced the lowest RMSE, which is consistent with its superior in-sample fit (R2 = 0.904), but both models showed sufficient forecasting accuracy. This demonstrates how well the machine learning model captures intricate, non-linear interactions.