linearmodels.system.covariance.GMMKernelCovariance¶

class linearmodels.system.covariance.GMMKernelCovariance(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, kernel: str = 'bartlett', bandwidth: float | 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

kernel: str = 'bartlett'¶

Name of kernel to use. Supported kernels include:

• ”bartlett”, “newey-west” : Bartlett’s kernel

• ”parzen”, “gallant” : Parzen’s kernel

• ”qs”, “quadratic-spectral”, “andrews” : Quadratic spectral kernel

bandwidth: float | None = None¶

Bandwidth to use for the kernel. If not provided the optimal bandwidth will be estimated.

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 \(\Omega\) is the covariance of the moment conditions.

Methods

Properties

bandwidth	Bandwidth used in estimation
cov	Parameter covariance
cov_config	Optional configuration information used in covariance
kernel	Kernel used in estimation