The Impact of Digitalization on Carbon Emission Efficiency: An Intrinsic Gaussian Process Regression Approach

This study introduces an intrinsic Gaussian Process Regression (iGPR) model for the first time, which incorporates non-Euclidean spatial covariates via a Gaussian process prior to analyzing the relationship between digitalization and carbon emission efficiency. The iGPR model’s hierarchical design embeds a Gaussian process as a flexible spatial random effect with a heat-kernel-based covariance function to capture the manifold geometry of spatial features. To enable tractable inference, we employ a penalized maximum-likelihood estimation (PMLE) approach to jointly estimate regression coefficients and covariance hyperparameters. Using a panel dataset linking a national digitalization (modernization) index to carbon emission efficiency, the empirical analysis demonstrates that digitalization has a significantly positive impact on carbon emission efficiency while accounting for spatial heterogeneity. The iGPR model also exhibits superior predictive accuracy compared to state-of-the-art machine learning methods (including XGBoost, random forest, support vector regression, ElasticNet, and a standard Gaussian process regression), achieving the lowest mean squared error (MSE = 0.0047) and an average prediction error near zero. Robustness checks include instrumental-variable GMM estimation to address potential endogeneity across the efficiency distribution and confirm the stability of the estimated positive effect of digitalization.