linearmodels.system.covariance.GMMHomoskedasticCovariance

class GMMHomoskedasticCovariance(x, z, eps, w, *, sigma=None, debiased=False, constraints=None)

Covariance estimator for IV system estimation with homoskedastic data

Parameters

xList[ndarray]

List containing the model regressors for each equation in the system

zList[ndarray]

List containing the model instruments for each equation in the system

epsndarray

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

wndarray

Weighting matrix used in estimation

sigmandarray

Residual covariance used in estimation

constraints{None, LinearConstraint}

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

Attributes

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

Methods

Properties

cov	Parameter covariance
cov_config	Optional configuration information used in covariance