Assessing two common approaches for solving models with saddle-path instabilities

This paper presents an approach for assessing the time taken by the well known reverse-shooting and forward-shooting algorithms to solve large-scale macroeconomic models characterized by saddle-path instability. We focus on a range of investment models with multi-dimensional specifications of the capital stock. Each algorithm presents a complicated exercise with a potentially unstable ordinary differential equation to be solved over a wide parameter space and involving a difficult search. Our results provide insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models. We describe how econometric techniques could be used to summarize the likely success of competing algorithms when confronted with models exhibiting a range of properties.