This paper provides a synthesis and further development of a global modelling approach introduced in Pesaran, Schuermann and Weiner (2004), where country specific models in the form of VARX* structures are estimated relating a vector of domestic variables, xit, to their foreign counterparts, x*it, and then consistently combined to form a Global VAR (GVAR). It is shown that the VARX* models can be derived as the solution to a dynamic stochastic general equilibrium (DSGE) model where over-identifying long-run theoretical relations can be tested and imposed if acceptable. This gives the system a transparent long-run theoretical structure. Similarly, short-run over-identifying theoretical restrictions can be tested and imposed if accepted. Alternatively, if one has less confidence in the short-run theory the dynamics can be left unrestricted. The assumption of the weak exogeneity of the foreign variables for the long-run parameters can be tested, where x*it variables can be interpreted as proxies for global factors. Rather than using deviations from ad hoc statistical trends, the equilibrium values of the variables reflecting the long-run theory embodied in the model can be calculated. This approach has been used in a wide variety of contexts and for a wide variety of purposes. The paper also provides some new results.