# linearmodels.system.covariance.GMMKernelCovariance¶

class GMMKernelCovariance(x, z, eps, w, *, sigma=None, debiased=False, constraints=None, kernel='bartlett', bandwidth=None)[source]

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

Constraints used in estimation, if any

kernelstr

Name of kernel to use. Supported kernels include:

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

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

bandwidthfloat

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.

Attributes
bandwidth

Bandwidth used in estimation

cov

Parameter covariance

cov_config

Optional configuration information used in covariance

kernel

Kernel used in estimation

Methods

Properties

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