gEconpy.model.model.Model.steady_state

Model.steady_state(how='analytic', use_jac=True, use_hess=True, use_hessp=False, progressbar=True, optimizer_kwargs=None, verbose=True, bounds=None, fixed_values=None, jitter_x0=False, **updates)

Solve for the deterministic steady state of the DSGE model.

A steady state is defined as the fixed point in the system of nonlinear equations that describe the model’s equilibrium. Given a system of model equations \(F(x_{t+1}, x_t, x_{t-1}, \varepsilon_t)\), the steady state is defined as a state vector \(\bar{x}\) such that

\[F(\bar{x}, \bar{x}, \bar{x}, 0) = 0\]

where \(0\) is the zero vector. At the point \(\bar{x}\), the system will not change, absent an exogenous shock.

The steady state is a key concept in DSGE modeling, as it is the point around which the model is linearized.

Parameters:

how: str, one of [‘analytic’, ‘root’, ‘minimize’], default: ‘analytic’

Method to use to solve for the steady state. If 'analytic', the model is solved analytically using user-provided steady-state equations. This is only possible if the steady-state equations are fully defined. If 'root', the steady state is solved using a root-finding algorithm. If 'minimize', the steady state is solved by minimizing a squared error loss function.

use_jac: bool, default: True

Flag indicating whether to use the Jacobian of the error function when solving for the steady state. Ignored if how is ‘analytic’.

use_hess: bool, default: False

Flag indicating whether to use the Hessian of the error function when solving for the steady state. Ignored if how is not ‘minimize’

use_hessp: bool, default: True

Flag indicating whether to use the Hessian-vector product of the error function when solving for the steady state. This should be preferred over use_hess if your chosen method supports it. For larger problems it is substantially more performant. Ignored if how not “minimize”.

progressbar: bool, default: True

Flag indicating whether to display a progress bar when solving for the steady state.

optimizer_kwargs: dict, optional

Keyword arguments passed to either scipy.optimize.root or scipy.optimize.minimize, depending on the value of how. Common argments include:

• ‘method’: str,

  The optimization method to use. Default is 'hybr' for how = 'root' and trust-krylov for how = 'minimize'

• ‘maxiter’: int,

  The maximum number of iterations to use. Default is 5000. This argument will be automatically renamed to match the argument expected by different optimizers (for example, the 'hybr' method uses maxfev).

verbose: bool, default True

If true, print a message about convergence (or not) to the console .

bounds: dict, optional

Dictionary of bounds for the steady-state variables. The keys are the variable names and the values are tuples of the form (lower_bound, upper_bound). These are passed to the scipy.optimize.minimize function, see that docstring for more information.

fixed_values: dict, optional

Dictionary of fixed values for the steady-state variables. The keys are the variable names and the values are the fixed values. These are not check for validity, and passing an inaccurate value may result in the system becoming unsolvable.

jitter_x0: bool

Whether to apply some small N(0, 1e-4) jitter to the initial point

**updates: float, optional

Parameter values at which to solve the steady state. Passed to self.parameters. If not provided, the default parameter values (those originally defined during model construction) are used.

Returns:

steady_state: SteadyStateResults

Dictionary of steady-state values