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FiPIt: A Simple, Fast Global Method for Solving Models with Two Endogenous States & Occasionally Binding Constraints


  • Enrique G. Mendoza
  • Sergio Villalvazo


We propose a simple and fast fixed-point iteration algorithm FiPIt to obtain the global, non-linear solution of macro models with two endogenous state variables and occasionally binding constraints. This method uses fixed-point iteration on Euler equations to avoid solving two simultaneous nonlinear equations (as with the time iteration method) or creating modified state variables requiring irregular interpolation (as with the endogenous grids method). In the small-open-economy RBC and Sudden Stops models provided as examples, FiPIt is used on the bonds and capital Euler equations to solve for the bonds decision rule and the capital pricing function. In a standard Matlab platform, FiPIt solves both models much faster than time iteration and various hybrid methods. The choice of functions that FiPIt iterates on using the Euler equations can vary across models, and there can be more that one arrangement for the same model.

Suggested Citation

  • Enrique G. Mendoza & Sergio Villalvazo, 2019. "FiPIt: A Simple, Fast Global Method for Solving Models with Two Endogenous States & Occasionally Binding Constraints," NBER Working Papers 26310, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:26310
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    JEL classification:

    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • F34 - International Economics - - International Finance - - - International Lending and Debt Problems
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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