Traditional models in spatial econometrics utilize a spatial weight matrix as a means to express spatial dependence, but its choice is quite arbitrary. Besides, it imposes a linear structure between dependent variables; in its simplest form, a dependent variable at one spatial unit is alinear combination of dependent variables at other spatial units (see LaSage and Pace (2009), Elhorst (2014)) among others). When the underlying disturbance distribution is assumed to be Gaussian or elliptical in general, the model does not allow asymmetry in dependence structure and tail dependence for spatial interactions. These restrictions are too strict in some applications, for example, to financial data such as market indexes and exchange rates for several countries (c.f. Kou et al. (2018)). In this study, therefore, we generalize existent models to allow for some nonlinear and tail dependence in dependent variables by employing copula approach to the disturbance distribution; Using a skew-t copula for example (Yoshiba (2018)), we may capture nonlinear and tail dependence which cannot be detected by linear models. After discussing some properties of the resulting model, we develop an estimation method both for parametric and semiparametric model. For parametric models, we can use either full maximum likelihood method or the method of inference function for margins. Semiparametric estimation of dependence parameters in parametric copulas without any knowledge of marginal distributions is another possibility. We then apply our recent resampling procedures with the empirical beta copula to compute confidence intervals. Simulation results illustrate the applicability of our procedure, and some real applications to financial data will be given. Possibility of extensions by accommodating exogenous explanatory variables and observable endogenous weighting matrix (a la Kelejian and Piras (2018)) will be discussed.
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