Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method

I propose a Galerkin projection method for solving dynamic economic models with many state variables. This method employs non-product monomial integration formulas for the computation of weighted residuals, and its computational cost therefore increases only polynomially in the model's dimensionality. I illustrate the practical implementation of the proposed algorithm by solving several specifications of the multi-country Real Business Cycle model described in Den Haan et al. [2010. Computational suite of models with heterogeneous agents: multi-country Real Business Cycle models. Journal of Economic Dynamics and Control, this issue], and briefly discuss two possible routes for further improving its numerical accuracy.