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 1st order VAR model for yk is:
Where ak is an N-vector of fixed effects, and B, C, D and F are diagonal NxN matrices with e.g. bkin along the leading diagonal of Bk. In the homogeneous case bkin = bk. 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 uki and ukn, i.e. within variables, but not between them. So uk and uj 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.