**SpVAR Procedure**

Let be an N-vector for variable k = 1,2,..K where N is the number of spatial units. Let where W denotes the special connectivity matrix. The 1^{st} order VAR model for y_{k} is:

Where a_{k} is an N-vector of fixed effects, and B, C, D and F are diagonal NxN matrices with e.g. b_{kin} along the leading diagonal of B_{k}. In the homogeneous case b_{kin} = b_{k}. B and D comprise autoregressive parameters within and between variables respectively. C and F comprise their SAR counterparts.

- Equation (1) is estimated for each variable using the panel data procedure in Eviews. If the SUR option is used, estimation takes account of correlation between u
_{ki}and u_{kn}, i.e. within variables, but not between them. So u_{k}and u_{j}are assumed to be uncorrelated. - The K estimated model objects from #1 are saved in the make model procedure in Eviews. Also the identities for the spatial lags were saved to construct the SpVAR model.
- A full dynamic simulation (FDS) of the SpVAR model was carried out to form a baseline for all state variables.
- The FDS baseline was shocked by perturbing the SpVAR innovations for variable j using add factors to form "scenarios".
- The spatio-temporal impulse responses are defined as the difference between the scenario solution for perturbing variable j and the FDS solution from #4.