We introduce a new model for time-varying spatial dependence. The model extends the well-known static spatial lag model. All parameters can be estimated conveniently by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimator for the static parameters is consistent and asymptotically normal. We also study the information theoretic optimality of the updating steps for the time-varying spatial dependence parameter. We adopt the model to empirically investigate the spatial dependence between eight European sovereign CDS spreads over the period 2009--2014, which includes the European sovereign debt crisis. We construct our spatial weight matrix using cross-border lending data and include country-specific and Europe-wide risk factors as controls. We find a high, time-varying degree of spatial spillovers in the sovereign CDS spread data. There is a downturn in spatial dependence after the first half of 2012, which is consistent with policy measures taken by the European Central Bank. The findings are robust to a wide range of alternative model specifications.
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