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
Parameter covariance
Optional configuration information used in covariance