linearmodels.iv.covariance.HeteroskedasticCovariance

class HeteroskedasticCovariance(x, y, z, params, debiased=False, kappa=1)[source]

Covariance estimation for heteroskedastic data

Parameters
xndarray

Model regressors (nobs by nvar)

yndarray

Series ,modeled (nobs by 1)

zndarray

Instruments used for endogenous regressors (nobs by ninstr)

paramsndarray

Estimated model parameters (nvar by 1)

debiasedbool

Flag indicating whether to use a small-sample adjustment

kappafloat

Value of kappa in k-class estimator

Notes

Covariance is estimated using

\[n^{-1} V^{-1} \hat{S} V^{-1}\]

where

\[\hat{S} = n^{-1} \sum_{i=1}^n \hat{\epsilon}_i^2 \hat{x}_i^{\prime} \hat{x}_i\]

where \(\hat{\gamma}=(Z'Z)^{-1}(Z'X)\) and \(\hat{x}_i = z_i\hat{\gamma}\). If debiased is true, then \(S\) is scaled by n / (n-k).

\[V = n^{-1} X'Z(Z'Z)^{-1}Z'X\]

where \(X\) is the matrix of variables included in the model and \(Z\) is the matrix of instruments, including exogenous regressors.

Attributes
config
cov

Covariance of estimated parameters

debiased

Flag indicating if covariance is debiased

s

Heteroskedasticity-robust score covariance estimate

s2

Estimated variance of residuals.

Methods

Properties

config

cov

Covariance of estimated parameters

debiased

Flag indicating if covariance is debiased

s

Heteroskedasticity-robust score covariance estimate

s2

Estimated variance of residuals.