We extend the well-known static spatial Durbin model by introducing a time-varying spatial dependence parameter. The updating steps for this model are functions of past data and have information theoretic optimality properties. The static parameters are conveniently estimated by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimators of the static parameters are consistent and asymptotically normal. Using spatial weights based on cross-border lending data and European sovereign CDS spread data over the period 2009–2014, we find evidence of contagion in terms of high, time-varying spatial spillovers in the perceived credit riskiness of European sovereigns during the sovereign debt crisis. We find a particular downturn in spatial dependence in the second half of 2012 after the outright monetary transactions policy measures taken by the European Central Bank. Earlier non-standard monetary operations by the ECB did not induce such changes. The findings are robust to a wide range of alternative model specifications.