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[IrisToolbox] for Macroeconomic Modeling

Practical tricks for nonlinear models

jaromir.benes@iris-toolbox.com

Practical problems operating (larger) nonlinear models

  • Difficult to tell if the problem is imperfection of the numerical algorithm, or the simulation reaching out of the corridor of stability

  • Use auxiliary devices to make convergence happen, and to measure the extent of the pressures

False slope

  • Occasionally binding constraints, e.g. zero interest floor
\[ r_t = \max\left\{ 0, \, r_t^\mathrm{unc} \right\} \]

  • The discontinuity at the edge pose relatively little difficulties

  • The zero slope of the max or min functions in the binding regions is a more serious problem

Pressure relief valves (PRVs)

  • Augment structural ("behavioral") equations with terms that relieve the equations of the pressures created by nonlinearities

  • Control the PRV through a knob parameter

Examples

  • Zero interest floor and aggregate demand: \(\alpha \left( r_t - r^\mathrm{unc} \right)\)

  • Recapitalization when capital adequacy is damaged across the entire sector