Modeling foreign investment effects on latent environmental pressure: a cross-validated nonlinear framework

This study asks how the environmental consequences of foreign investment should be modeled when the outcome is multidimensional, only imperfectly observable, and shaped by nonlinear and temporally evolving interactions. Focusing on Pakistan over the period 1995–2023, we treat environmental pressure as a composite construct and examine its relationship with Chinese foreign direct investment, income per capita, trade openness, technological innovation, economic structural complexity, and geopolitical risk. Methodologically, the paper combines cross-validated artificial neural networks optimized through a genetic algorithm with long short-term memory models. This framework is designed to recover higher-order nonlinearities, interaction effects, and temporal dependence without imposing restrictive functional-form assumptions. The results indicate that the investment–environment nexus is not well described by a constant marginal effect. Instead, the association between inward Chinese investment and environmental pressure is curved, state-dependent, and mediated by the broader structural context. The contribution of investment appears limited in simpler mappings but becomes stronger when variables are combined through deeper nonlinear interactions. The sequence-based results further suggest that temporal dependence matters and that the estimated patterns remain stable under out-of-sample validation. Overall, our findings support a methodological shift away from single-indicator, linear specifications toward more flexible approaches that can model latent environmental outcomes and heterogeneous adjustment processes.