Worked examples¶

Eight worked-out model folders ship with the source tree under examples/. Each folder is self-contained:

a common.mod with the shared declarations, model and steady_state_model, included via @#include by each scenario,
one or more scenario .mod files that differ only in their initval, shocks and simulate blocks,
a run_*.py script that solves every scenario through the Python API and writes an overlaid plot,
a README.md presenting the model, the experiments and the simulation results, with embedded plots.

One folder, examples/nk-nonlinear/, departs from this layout: its variants differ in the equations themselves, so they ship as self-contained .mod files with no shared common.mod.

Run any scenario with the CLI or the API exactly as in the Quick start. The list below points at the headline result of each.

Saddle-path models (one state + one jump)¶

examples/rbc/: Ramsey/RBC with two state variables (capital and an Ornstein– Uhlenbeck productivity process), one jump (consumption) and one algebraic (output). Showcases the multi-segment surprise machinery (rbc_anticipated vs rbc_surprise) and the e={…} anchor (rbc_sustained).
examples/dornbusch/: Dornbusch (1976) exchange-rate overshooting. Sticky price (state) + exchange rate (jump). Shows the classic impact overshoot under an unanticipated monetary expansion; anticipated and gradual variants dampen it.
examples/tobinq/: Tobin’s q investment with convex adjustment costs. Capital (state) + shadow value q (jump) + investment (algebraic). Anticipated vs surprise vs unanticipated profitability shocks; q jumps at the reveal time.

Pure forward-looking models (jumps only, no state)¶

examples/cagan/: Cagan model of money and prices: a single jump (the price level) driven by an exogenous money path. Prices LEAD anticipated money; the surprise variant shows prices flat until the reveal. Headline showcase for the shock-shape helpers (step, ramp).
examples/nk/: Continuous-time New Keynesian liquidity trap (Werning, 2011). Output gap and inflation (both jumps); the policy rate is max(0, …) — an occasionally-binding ZLB. A longer expected trap deepens today’s recession (forward-looking amplification).
examples/nk-nonlinear/: The fully nonlinear continuous-time New Keynesian model in levels — the nonlinear companion to examples/nk/ (which carries the log-linearised trap). Three self-contained variants driven by the same TFP shock: baseline (no habits), external_habit, and internal_habit (the last internalises habits, adding a costate — a state — so only this variant steps outside “jumps only”). The policy rate keeps the ZLB kink directly in levels. The full derivations — household and Rotemberg firm problems, both habit variants, every steady state — are in a Beamer companion: nk-nonlinear.pdf.

Pure initial-value problems (states only, no jump)¶

examples/solow/: Solow–Swan growth: one state (capital), no jump. The simplest example; scenarios are convergence-from-below, a permanent savings-rate rise, and a permanent productivity rise.
examples/goodwin/: Goodwin (1967) growth cycle: a Lotka–Volterra system in two states (employment and the wage share). The interior fixed point is a centre, so the trajectory is a closed orbit — there is no terminal boundary condition (no jumps to anchor) and history alone pins the path. Scenarios vary the initial amplitude.

Each folder’s README has the model equations, parameter values, references, and a brief discussion of the simulated dynamics.

A few folders also ship auxiliary runners behind the figures in this manual: examples/goodwin/run_schemes.py (the scheme/order accuracy comparison of Discretisation schemes), examples/rbc/run_adapt.py (the adaptive-refinement run of Time grids and adaptive refinement), and examples/benchmark_solvers.py (the linear-solver timings of Linear solvers).