Approximately Right?: Global v. Local Methods for Open-Economy Models with Incomplete Markets

Abstract

Global and local methods are widely used in international macroeconomics to analyze incompletemarkets models. We study solutions for an endowment economy, an RBC model and a Sudden Stops model with an occasionally binding credit constraint. First-order, second-order, risky steady state (RSS), and DynareOBC solutions are compared v. xed-point-iteration global solutions in the time and frequency domains. The solutions dier in key respects, including measures of precautionary savings, cyclical moments, impulse response functions, nancial premia and macro responses to credit constraints, and periodograms of consumption, foreign assets and net exports. The global method is easy to implement and fast albeit slower than local methods, except DynareOBC which is of comparable speed. These ndings favor global methods except when prevented by the curse of dimensionality and urge caution when using local methods. Of the latter, rst-order solutions are preferable because results are very similar to second-order and RSS methods. JEL Classication: F41, E44, D82 . The views expressed in this paper are those of the authors and should not be attributed to the Board of Governors of the Federal Reserve System or its sta. not reported. In calibrated cases (three research papers and three policy models), ψ is in the 0.01-0.1 range, and in estimated cases (four research papers and one policy model), the point estimates or the medians of posterior distributions in Bayesian estimation are in the 0.00014-2.8 range.While global methods have the advantage that the models are solved in their original form and capture the dynamics of wealth accurately, they suer from the traditional curse-of-dimensionality problem: They are impractical in large models because the methods become exponentially inecient 2 Garcia-Cicco et al. (2010) explain that, following Schmitt-Grohé and Uribe (2003), the standard practice is to set ψ to a small value because the DEIR function aims to obtain independence of the deterministic steady state from initial conditions without aecting cyclical dynamics. They also studied a model in which ψ represents nancial frictions, and in this case they estimated ψ using Bayesian methods.3 Note, however, that the DEIR functional forms are not always the same, so ψ values are not directly comparable.When relevant for our quantitative analysis, we control for this by making comparisons in terms of the elasticity of the interest rate with respect to percent deviations of NFA from steady state.2 as the number of endogenous state variables rises. The local methods have the advantage that they can be applied in large-scale models, but have the shortcoming that they need the stationarityinducing assumptions that are not part of the original models, and more importantly, as we show in this paper, these extra assumptions may not be innocuous for the numerical results. Hence, these tradeos pose two key questions: Under what conditions are local solutions better approximations to the exact solutions obtained with global methods? When those c...

Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints

“…de Groot et al (2019) compare the performance of local approximations and EPFP methods with the global solution of open-economy models with incomplete markets and occasionally binding borrowing constraints. Their results show that simulated moments from local and EPFP methods can differ substantially from those obtained using global solutions and advise in favor of solving this class of models using the original nonlinear equilibrium conditions.…”