This paper studies the variable selection of high-dimensional spatial autoregressive panel models with fixed effects in which a matrix transformation method is applied to eliminate the fixed effects. Then, a penalized quasi-maximum likelihood is developed for variable selection and parameter estimation in the transformed panel model. Under some regular conditions, the consistency and oracle properties of the proposed estimator are established. Some Monte-Carlo experiments and a real data analysis are conducted to examine the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.

Achieving “dual carbon” targets by containing carbon emissions while sustaining economic growth is challenging. This study examines the varying carbon dependency levels among China’s 30 provincial-level administrative units, considering spatial correlations in emissions. Using a semi-parametric varying coefficient spatial autoregressive panel model on 2004–2019 panel data, this study shows the following: (i) The relationship between economic growth and carbon emissions forms an “S”-shaped curve, with the contribution decreasing as tertiary industry grows, defining three stages of carbon dependency. (ii) There is significant heterogeneity in carbon dependency across provinces, with some advancing to “weak dependency” or an “economic carbon peak” due to advantages and policies. (iii) Dependency levels shift over time, with “weak dependency” being the predominant stage, though transitions occur. (iv) A positive spatial spillover effect in emissions was noted. This study recommends tailored policies for each provincial-level administrative unit based on their carbon dependency and development stage.

Heteroscedasticity is often encountered in spatial-data analysis, so a new class of heterogeneous spatial autoregressive models is introduced in this paper, where the variance parameters are allowed to depend on some explanatory variables. Here, we are interested in the problem of parameter estimation and the variable selection for both the mean and variance models. Then, a unified procedure via double-penalized quasi-maximum likelihood is proposed, to simultaneously select important variables. Under certain regular conditions, the consistency and oracle property of the resulting estimators are established. Finally, both simulation studies and a real data analysis of the Boston housing data are carried to illustrate the developed methodology.

This paper proposes a variable selection method for a semiparametric varying coefficient spatial autoregressive panel model with fixed effects based on a penalized profile quasi-likelihood method, which can simultaneously select significant variables in parametric components and nonparametric components without estimating fixed effects. With an appropriate selection of the tuning parameters and some mild assumptions, the consistency of this procedure and the oracle property of the obtained estimators are established. Then, we conduct some Monte Carlo simulations to assess the finite sample performance of the proposed variable selection method, and finally, we analyze a real dataset for further illustration.