Assessing two common approaches for solving models with saddle-path instabilities
Mathematics and Computers in Simulation - Special issue: Second special issue: Selected papers of the MSSANZ/IMACS 15th biennial conference on modelling and simulation
Solving Non-Linear Models with Saddle-Path Instabilities
Computational Economics
Comparing different approaches for solving optimizing models with significant nonlinearities
Mathematics and Computers in Simulation
Solving macroeconomic models with "off-the-shelf" software: An example of potential pitfalls
Mathematics and Computers in Simulation
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In this paper, we consider a macroeconomic model with alternative linear and non-linear specifications. One version of the model, expressed in levels, is highly non-linear and has at least two steady-state equilibria. One of these equilibria has an economically meaningful interpretation, while the other does not have a sensible economic interpretation. A second version of the model, expressed in logarithms, is linear and has a unique steady-state equilibrium, which corresponds to the economically meaningful equilibrium of the non-linear version of the model. The dynamic solution of each model version has a combination of stable and unstable eigenvalues so that any dynamic solution requires the calculation of appropriate ''jumps'' in endogenous variables. Attempts to solve these models, using forward-shooting and reverse-shooting algorithms, show that the forward-shooting algorithm chooses the ''wrong'' solution for the non-linear model, but the ''right'' solution for the linear model. The reverse-shooting algorithm chooses the ''right'' solution in both cases. We demonstrate how this result is driven by particular properties of the two versions of the model.