Solving Models with Off-the-Shelf Software: An Example of Potential Pitfalls Associated with the Use and Abuse of Default Parameter Settings

When working with large-scale models or numerous small models, there can be a temptation to rely on default settings in proprietary software to derive solutions to the model. In this paper we show that, for the solution of non-linear dynamic models, this approach can be inappropriate. We consider a simple linear model with two stable eigenvalues (real-valued or complex-valued) and one unstable eigenvalue (real-valued). The chosen model is an extended version of a model previously described by Turnovsky (2000). It can be derived from the Sargent and Wallace (1973) extension of the Cagan (1956) model by adding a labour market defined by both employment and wages and by introducing sluggish adjustment for both these variables. We choose parameters for the model. The configuration of eigenvalues can be changed by choosing alternative parameter values. It is possible to choose parameter configurations that generate complex-valued eigenvalues and real-valued eigenvalues. For this paper we focus on the real-valued eigenvalues. Alternative linear and non-linear specifications of the model are examined. One version of the model, expressed in levels, is highly non-linear. A second version of the model, expressed in logarithms, is linear. 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