Solution Methods

RunDynam offers the same variety of solution methods as is offered by GEMPACK: for an introduction and more details, see the GEMPACK mnaual chapter Multi-step solution methods or look online at www.copsmodels.com/gpmanual.htm#gpd3.7 .

•The SINGLE-STEP SOLUTION, or Johansen method, treats the model as a linear system, linearized around the initial solution. This approach is the simplest and quickest to compute. However, since the model is actually a non-linear system, Johansen results are not quite accurate, except for small shocks. The errors are super-proportional to the size of the shock: double the size of the shock, and the size of the error will more than double.

•MULTI-STEP SOLUTION procedures are used to reduce linearization errors which arise from the default one-step or Johansen solution method. Briefly, the Euler multi-step procedure automatically divides the exogenous shock into a (user-specified) number of equal components. For example, a 10% increase in labour supply might be computed as two successive increases of 4.88% (1.0488 x 1.0488 = 1.1). Results for the first 4.88% instalment are calculated and the database is updated accordingly. Using the new database, results are calculated for the second 4.88% instalment. Since errors are super-proportional to the size of the shock, halving the shock leads to errors at each step which are less than half the size of the error produced by a single, full-size, step. Thus, the results from the two steps may be combined to produce a solution which is more accurate than that obtained by a single step. The more steps, the more accuracy. The Gragg and Midpoint methods are variations on the Euler method which can sometimes produce more accurate results for a given number of steps.

•SEQUENCE OF SOLUTIONS WITH EXTRAPOLATION—Early experiments in solving models by the Euler method led to the following observations. The differences between a 8-step and a 16-step solution are often about half those between a 4-step and an 8-step solution. The differences between a 16-step and a 32-step solution are about half those between a 8-step and a 16-step solution, and so on. This rule enables us to predict what results would be generated by a solution with an infinite number of steps—that is, the exact solution. For example, we might choose to run 3 Euler solutions with respectively 4, 8 and 12 steps. GEMPACK automatically uses these results to extrapolate to a solution that is more accurate than any of the 3 individual solutions. For Gragg and Midpoint methods the numbers of steps in a sequence of solutions must be either all odd or all even. You may use Automatic Accuracy in this case.

See the GEMPACK User documentation for more details about the different possibilities.

URL of this topic: www.copsmodels.com/webhelp/rundynam/hc_solmethod.htm

Link to full GEMPACK Manual

Link to GEMPACK homepage