The paper investigates the relative importance of exchange rates as determinants of economic growth, a topic largely unexplored using nonparametric methods. Existing literature firmly establishes the negative impact of poor exchange rate policies, yet the relative importance of exchange rates remains unclear. Rodrik (2008) found that exchange rate undervaluation stimulates growth in developing countries, but questions remain regarding the relevance of undervaluation across different economies and functional relationships. Easterly (2003) highlighted the negative effects of overvaluation, linking it to macroeconomic instability. Subsequent studies, mostly employing parametric methods (GMM, etc.), analyzed the real exchange rate-growth relationship. This study addresses this gap by applying machine learning techniques to evaluate Rodrik's findings in Germany, Slovakia, and South Africa, representing developed, developing, and emerging economies, respectively. The contributions are twofold: validating Rodrik's findings using nonparametric techniques and determining the optimal machine learning model (PSO vs. GA) for each country.

Numerous studies have examined the real exchange rate and economic growth. Some focus on the impact of exchange rate regimes (Levy-Yeyati and Sturzenegger, 2003; Harms and Kretschmann, 2009; others on the real exchange rate-growth linkage (Tharakan, 1999; Rodrik, 2008; Tarawalie, 2010). Most employ parametric methods. This study is novel in its application of machine learning (PSO, GA, feature selection) to analyze this relationship, offering a nonparametric perspective that avoids distributional assumptions and reduces estimation costs.

The study uses Rodrik's (2008) model, which relates GDP growth to initial income per capita and undervaluation, incorporating country and time dummies. Undervaluation is calculated using the Balassa-Samuelson effect. The authors employed machine learning due to the nonlinear relationships indicated by the Ramsey Reset Test. The methodology includes: 1. **Feature Selection (Multilayer ANN):** A multilayer artificial neural network is used as a feature selection method to identify the most important variables influencing economic growth. The model uses a generalized delta rule for weight adjustment. 2. **PSO (Particle Swarm Optimization):** PSO is a continuous optimization technique that simulates the social behavior of swarms. The algorithm iteratively adjusts the position and velocity of particles in the solution space to find the optimal solution, in this case improving the accuracy of the Rodrik model. 3. **GA (Genetic Algorithm):** GA is another optimization technique based on natural selection principles. It involves selection, crossover, and mutation processes to evolve a population of solutions towards an optimal solution. The study compares the performance of PSO and GA in optimizing the Rodrik model for each country.

The study used annual data from the World Bank Database (1990-2016) for Germany, South Africa, and Slovakia. Table 1 presents the results of PSO and GA optimization for each country. For Germany, PSO showed a lower standard error (0.084636) compared to GA (0.15645), indicating better model fit. For South Africa, GA performed better (0.081297 vs 0.09148). For Slovakia, PSO showed better results, but the model could not be well fit due to data limitations. Feature selection (Table 2) revealed that GDP per capita is the most influential factor for Germany and South Africa, while undervaluation is most important for Slovakia. The findings support Rodrik's conclusion that undervaluation does not significantly influence growth in Germany and South Africa but contradict his conclusion for a developed country like Slovakia with high trade openness. Slovakia's high growth and trade openness contrast with Germany's performance.

The findings suggest that the importance of exchange rates in influencing economic growth is contingent upon the level of trade openness. In highly open economies, exchange rate policies (like undervaluation) are crucial. In less open economies, improving income per capita is more important. The differences in the tradable sector size and dynamics between countries like Germany and Slovakia, despite both being developed, can account for the conflicting results. South Africa's underdeveloped tradable sector further explains the findings. The study provides valuable insights for policymakers in both developed and developing countries in setting exchange rate and economic growth targets.

This study is the first to employ machine learning techniques to analyze the real exchange rate-economic growth relationship, offering a nonparametric approach. The findings demonstrate the conditional relevance of exchange rate policies, depending on trade openness. Highly open economies should prioritize exchange rate policies, while less open economies should focus on income per capita. Future research could explore other factors that influence this relationship and investigate broader economic implications of the findings.

The study is limited by the availability of data and model selection for Slovakia, the selection of only three countries may not fully reflect global diversity, and the chosen machine learning methods might not be suitable for all types of economic data.