Spatial Vector Autoregressions

A spatial vector autoregression (SpVAR) is a panel VAR in which the data happen to be spatial. SpVARs include the temporal lags of spatial lagged dependent variables in their specification. SpVARs generate spatiotemporal impulse responses in which shocks to specific variables in specific locations diffuse over time and across space for the variable concerned as well as other variables. To fix ideas, a “toy” model is used in which there are two locations and only one variable. Subsequently, the numbers of locations and variables are generalized. An empirical illustration of an SpVAR for Israel is presented in which there are nine regions and four variables. The spatiotemporal impulse responses for the SpVAR are calculated assuming that the innovations are independent and assuming that they are spatially correlated. We argue that just as structural VAR models under-identify the structural parameters, the same applies to SpVARs. Hence, the epistemological value of SpVARs is doubtful. Nevertheless, SpVARs provide empirical descriptions of the data, which may serve as a benchmark for validating structural models, which are featured in Chap. 7.