Economic Complexity and Environmental Impact using a Neural-Network Embedded Semiparametric Mixture of Experts Model

The environmental Kuznets curve (EKC) postulates an inverted-U relationship between environmental quality and economic performance. Recent studies examine the EKC hypothesis across groups of countries (e.g., developing and OECD) by considering the impact of economic complexity (a measure of economic performance) on CO2 emissions (a measure of environmental quality). However, most of the studies impose, possibly, restrictive assumptions on the data: (1) all countries are assumed to follow the same developmental path and hence EKC; (2) the functional relationship between CO2 emissions and economic complexity is assumed to have a known parametric form. In this paper, we propose to relax these assumptions. First, we allow for the possibility that countries may follow different developmental paths by using the mixture of experts (MoE) approach. This gives rise to multiple EKCs. The MoE approach further allows us to endogenously identify different developmental paths and thus accounts for unobserved heterogeneity. Moreover, this approach allows us to probabilistically classify each country into any one of the obtained developmental paths. Second, we assume that the functional relationship between CO2 emissions and economic complexity is represented by a nonparametric (unknown) function of economic complexity. This allows the EKC the flexibility to take any form based on the data. Therefore, each expert regression model is a partially linear model (PLM). In contrast to existing PLMs, we allow the nonparametric part to be a multivariate function of any dimension. For model estimation, we propose a maximum likelihood estimation procedure through a hybrid algorithm that combines feed-forward neural networks (NN) with the classical expectation-conditional-maximization (ECM) algorithm, termed the ECM-NN algorithm. We use a simulation study to demonstrate the performance of this estimation procedure across various scenarios with different dimensions of the nonparametric function. Finally, we apply the proposed methods to a cross-country panel dataset of 64 countries spanning 2003 to 2022 and find two developmental paths in which the EKC holds.