Functional SAR models: With application to spatial econometrics

Simultaneous autoregressive (SAR) models have been extensively used for the analysis of spatial data in areas as diverse as demography, economy and geography. These are linear models with a scalar response, scalar explanatory variables and autoregressive errors. In this work we extend this modeling approach from scalar to functional covariates. Least squares and maximum likelihood are used as estimation methods of the parameters. A simulation study is considered for evaluating the performance of the proposed methodology. As an illustration, the model is used to establish the relationship between unsatisfied basic needs and curves of gross domestic product obtained in 32 departments of Colombia (districts of the country).