Pollution and Expenditures in a Penalized Vector Spatial Autoregressive Time Series Model with Data-Driven Networks

This paper introduces a Spatial Vector Autoregressive Moving Average (SVARMA) model in which multiple cross-sectional time series are modeled as multivariate, possibly fat-tailed, spatial autoregressive ARMA processes. The estimation requires specifying the cross-sectional spillover channels through spatial weights matrices. the paper explores a kernel method to estimate the network topology based on similarities in the data. It discusses the model and estimation, focusing on a penalized Maximum Likelihood criterion. The empirical performance of the estimator is explored in a simulation study. The model is used to study a spatial time series of pollution and household expenditure data in Indonesia. The analysis finds that the new model improves in terms of implied density, and better neutralizes residual correlations than the VARMA, using fewer parameters. The results suggest that growth in household expenditures precedes pollution reduction, particularly after the expenditures of poorer households increase; that increasing pollution is followed by reduced growth in expenditures, particularly reducing the growth of poorer households; and that there are significant spillovers from bottom-up growth in expenditures. The paper does not find evidence for top-down growth spillovers. Feedback between the identified mechanisms may contribute to pollution-poverty traps and the results imply that pollution damages are economically significant.