linearmodels.system.covariance.GMMHomoskedasticCovariance¶

class linearmodels.system.covariance.GMMHomoskedasticCovariance(x: list[numpy.ndarray], z: list[numpy.ndarray], eps: linearmodels.typing.data.Float64Array, w: linearmodels.typing.data.Float64Array, *, sigma: numpy.ndarray | None = None, debiased: bool = False, constraints: LinearConstraint | None = None)[source]¶

Covariance estimator for IV system estimation with homoskedastic data

Parameters:¶

x: list[numpy.ndarray]¶

List containing the model regressors for each equation in the system

z: list[numpy.ndarray]¶

List containing the model instruments for each equation in the system

eps: linearmodels.typing.data.Float64Array¶

nobs by neq array of residuals where each column corresponds an equation in the system

w: linearmodels.typing.data.Float64Array¶

Weighting matrix used in estimation

sigma: numpy.ndarray | None = None¶

Residual covariance used in estimation

constraints: LinearConstraint | None = None¶

Constraints used in estimation, if any

Notes

The covariance is estimated by

\[(X'ZW^{-1}Z'X)^{-1}(X'ZW^{-1}\Omega W^{-1}Z'X)(X'ZW^{-1}Z'X)^{-1}\]

where \(\Omega = W = Z'(\Sigma \otimes I_N)Z\) where m is the number of moments in the system

Methods

Properties

cov	Parameter covariance
cov_config	Optional configuration information used in covariance