This article considers some of the technical issues involved in using the global vector autoregression (GVAR) approach to construct a multi‐country rational expectations (RE) model and illustrates them with a new Keynesian model for 33 countries estimated with quarterly data over the period 1980–2011. The issues considered are: the measurement of steady states; the determination of exchange rates and the specification of the short‐run country‐specific models; the identification and estimation of the model subject to the theoretical constraints required for a determinate rational expectations solution; the solution of a large RE model; the structure and estimation of the covariance matrix and the simulation of shocks. The model used as an illustration shows that global demand and supply shocks are the most important drivers of output, inflation and interest rates in the long run. By contrast, monetary or exchange rate shocks have only a short‐run impact in the evolution of the world economy. The article also shows the importance of international connections, directly as well as indirectly through spillover effects. Overall, ignoring global inter‐connections as country‐specific models do, could give rise to misleading conclusions.