linearmodels.iv.covariance.ClusteredCovariance

class ClusteredCovariance(x, y, z, params, clusters=None, debiased=False, kappa=1)

Covariance estimation for clustered 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

clustersndarray

Cluster group assignment. If not provided, uses clusters of 1. Either nobs by ncluster where ncluster is 1 or 2.

kappafloat

Value of kappa in k-class estimator

Notes

Covariance is estimated using

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

where

\[\begin{split}\hat{S} & = n^{-1} (G/(G-1)) \sum_{g=1}^G \xi_{g}^\prime \xi_{g} \\ \xi_{g} & = \sum_{i\in\mathcal{G}_g} \hat{\epsilon}_i \hat{x}_i \\\end{split}\]

where \(\hat{\gamma}=(Z'Z)^{-1}(Z'X)\) and \(\hat{x}_i = z_i\hat{\gamma}\). \(\mathcal{G}_g\) contains the indices of elements in cluster g. If debiased is true, then \(S\) is scaled by g(n - 1) / ((g-1)(n-k)) where g is the number of groups..

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

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

Clustered estimator of score covariance

s2

Estimated variance of residuals.

Methods

Properties

config
cov	Covariance of estimated parameters
debiased	Flag indicating if covariance is debiased
s	Clustered estimator of score covariance
s2	Estimated variance of residuals.