Global v. Local Methods in the Quantitative Analysis of Open-Economy Models with Incomplete Markets

Two classes of numerical methods are widely used in International Macroeconomics to study incomplete markets models in which the dynamics of wealth distribution are state contingent, and the limiting distribution of wealth is influenced by precautionary savings behavior that induces large deviations from certainty equivalence. One class introduces assumptions that impose a unique deterministic steady state and uses local perturbation methods. The second solves directly for the stochastic steady state using global methods. We compare the solutions of canonical small open economy models produced by log-linear, second-order, and risk-adjusted steady state local methods assuming a debt-elastic world interest rate against those obtained using two global methods: A Bewley method with standard preferences and an interest rate lower than the rate of time preference, and an Uzawa-Epstein method with an endogenous rate of time preference. Comparing results in both the time and frequency domains yields two main findings. First, local methods produce good approximations only if they are calibrated using information from the global solutions. Second, even in this case they cannot approximate well all of the results of the global methods. These findings suggest caution in interpreting results obtained with local methods, and favor using global methods.