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A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.
Spatial regression models provide the opportunity to analyse spatial data and spatial processes. Yet, several model specifications can be used, all assuming different types of spatial dependence. This study summarises the most commonly used spatial regression models and offers a comparison of their performance by using Monte Carlo experiments. In contrast to previous simulations, this study evaluates the bias of the impacts rather than the regression coefficients and additionally provides results for situations with a non-spatial omitted variable bias. Results reveal that the most commonly used spatial autoregressive (SAR) and spatial error (SEM) specifications yield severe drawbacks. In contrast, spatial Durbin specifications (SDM and SDEM) as well as the simple SLX provide accurate estimates of direct impacts even in the case of misspecification. Regarding the indirect `spillover' effects, several - quite realistic - situations exist in which the SLX outperforms the more complex SDM and SDEM specifications.