PerturbationDSGE.solve

PerturbationDSGE.solve(theta)

Solve the model at a parameter point.

Parameters:

theta (ArrayLike) – Structural parameters in the model’s own space.

Return type:

_PerturbationSolution

Returns:

The _PerturbationSolution with the policy blocks h_x, g_x (and h_xx, g_xx, h_ss, g_ss at second order), the loading eta and the steady state.

Raises:

NumericalError – If the steady state does not solve the equations or the Blanchard-Kahn conditions fail.

Example

For the AR(1) latent state the first-order solution is the model itself:

>>> import numpy as np
>>> class Latent:
...     parameter_names, bounds = ("rho", "sigma"), ((0.0, 0.99), (0.01, 1.0))
...     n_states, n_controls = 1, 1
...     def equations(self, th, y_next, y, x_next, x):
...         return np.array([y[0] - x[0], x_next[0] - th[0] * x[0]])
...     def steady_state(self, th):
...         return np.zeros(1), np.zeros(1)
...     def shock_loading(self, th):
...         return np.array([[th[1]]])
...     def observation(self, th):
...         return np.array([[0.0, 1.0]]), np.zeros(1), np.array([[1e-4]])
...     def log_prior(self, th):
...         return 0.0
>>> solution = PerturbationDSGE(Latent(), np.zeros(50), order=1).solve([0.8, 0.5])
>>> solution.h_x.tolist(), solution.g_x.tolist(), solution.eta.tolist()
([[0.8]], [[1.0]], [[0.5]])
>>> solution.order, solution.is_stable, solution.n_shocks
(1, True, 1)