FactorAugmentedSVAR#

class cultivars.multivariate.structural.factor_augmented.FactorAugmentedSVAR(favar, structural=None, *, order=None)[source]#

Structural identification on a factor block, Bernanke-Boivin-Eliasz (2005).

Constructs with a fitted FAVAR result; the closed system being identified is its factor VAR, and the model adds what no factor-space scheme can: the observation-equation map onto the panel. Two ways in, one result out. By default identify runs the paper’s own scheme – recursive, observed block last, so the policy shock moves no factor within the period. Alternatively, identify the factor VAR yourself with any point-identified model in this package and pass what it returns as structural; the declaration then lives where you stated it, and this model only maps it.

Variables:

  • _source – The factor VAR being identified, favar.factors.

  • _favar – The fitted factor-augmented reduced form.

  • _structural – The supplied factor-space identification, or None for the recursive route.

  • _order – The recursive ordering, or None for factors first and the observed block last.

See also

References

Bernanke, B. S., Boivin, J., & Eliasz, P. (2005). Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach. Quarterly Journal of Economics, 120(1), 387-422.

Example

>>> import numpy as np
>>> from cultivars.multivariate.large_dim.factor_augmented import FAVAR
>>> rng = np.random.default_rng(0)
>>> factor = np.zeros(300)
>>> for t in range(1, 300):
...     factor[t] = 0.7 * factor[t - 1] + rng.standard_normal()
>>> panel = np.outer(factor, rng.uniform(0.5, 1.5, 30))
>>> panel += 0.3 * rng.standard_normal((300, 30))
>>> policy = 0.4 * factor + rng.standard_normal(300)
>>> res = FAVAR(panel, policy[:, None], n_factors=1, order=1).fit()
>>> svar = FactorAugmentedSVAR(res).identify()
>>> svar.impact.shape
(30, 2)

The mapping route takes an identification of this fit’s own factor VAR and refuses one built from another:

>>> from cultivars.multivariate.structural.zero_restrictions import RecursiveSVAR
>>> mine = RecursiveSVAR(res.factors).identify()
>>> bool(np.allclose(FactorAugmentedSVAR(res, mine).identify().impact, svar.impact))
True
>>> other = FAVAR(panel, policy[:, None], n_factors=1, order=2).fit()
>>> FactorAugmentedSVAR(res, RecursiveSVAR(other.factors).identify())
Traceback (most recent call last):
cultivars.exceptions.SpecificationError: the supplied identification was not built from ...

Attributes#

k_endog

Number of variables in the source system.

names

Variable labels of the source system.

source

The fitted reduced-form result being identified.

Methods#

identify()

Identify the factor system and bind the panel map to it.