Solving the multi-country real business cycle model using ergodic set methods

We apply the stochastic simulation algorithm, described in Judd, Maliar and Maliar (2009), and the projection cluster-grid algorithm, developed in Judd, Maliar and Maliar (2010a), to solving a collec-tion of multi-country models. Four techniques help us reduce the cost in high-dimensional problems: an endogenous grid enclosing the ergodic set, linear approximation methods, fixed-point iteration and efficient integration methods such as non-product monomial rules and Monte Carlo simulation combined with regression. We show that ac-curacy in intratemporal choice is crucial for the overall accuracy of so-lutions and offer two novel approaches, precomputation and iteration-on-allocation, that can solve for intratemporal allocations accurately and fast. We also propose a hybrid solution algorithm that combines the perturbation and accurate intratemporal-choice methods