An evaluation of alternative approaches to solving large-scale macroeconomic models.

This paper is concerned with assessing the time taken by the well known reverse-shooting and forward-shooting algorithms to solve large-scale macroeconomic models, which are characterized by having the particular property known as saddle-path instability. Given an arbitrary large-scale model about which we have limited information, how quick are the algorithms likely to be in solving this model? How are specific model properties likely to influence the time taken by a particular algorithm? We address this question using a range of investment models, which have been extended to allow for 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. There are a number of places where computational errors can be introduced and these errors can soon "blow-up". It is a good exercise on which to compare the two shooting methods. 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 also investigate additional questions that might be addressed in order to assess which approach is the best general way to find the stable trajectory of a model with saddle-path properties. 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.