Justification of spatial weights matrices and generalized Ⅳ estimation of SAR models
Spatial weights matrices are utilized to collect the cross-sectional relationship of different spatial units in spatial econometric models.Nevertheless,it is still very challenging in terms of the specification of spatial weights matrices in many real applications.In this paper,we justify a spatial weights matrix as a"bilateral channel/bridge"through the matrix decomposition with the violation of the tetra-difference condition based on existing researches.Two types of generalized Ⅳ estimation are proposed on the basis in the presence of time-varying and endogenous spatial weights matrices in spatial autoregressive(SAR)models,where the relevance assumption is easier to be satisfied with more detailed classification of variables in the weighting system for the first type;and the non-parametric specification of the error terms,uN=RNεN,is also generalized to the cases with stochastic elements in RN for the second type.Asymptotic properties of these methods are derived and small-sample performances of them are investigated through Monte Carlo simulations.Usefulness of the method is demonstrated in studying the spillover effects of air pollution through international trade in 92 countries(or areas).
instrumental variabletime-varying and endogenous spatial weights matricesspa-tial autoregressive(SAR)modelsair pollutionbilateral trade
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