Adaptive elastic net variable selection of spatial panel quantile autoregressive model with fixed effects

This paper proposes a variable selection method that combines instrumental variables and adaptive Elastic Net penalty for the spatial panel quantile autoregressive (SPQAR) model with fixed effects. This method can effectively identify key variables, estimate spatial effects, and address collinearity among variables while controlling for individual fixed effects. This paper gives the variable selection algorithm and establishes the large-sample properties of the penalized estimators. Numerical simulation results show that the adaptive Elastic Net method outperforms existing approaches in terms of estimation accuracy and variable selection precision, particularly under conditions of high collinearity and non-normal disturbances. Finally, this method is applied to analyze the impact of 13 explanatory variables on agricultural carbon emissions in China at different quantile levels. Both simulation and empirical results demonstrate the feasibility and effectiveness of the proposed method.