linearmodels.iv.covariance.ClusteredCovariance

class linearmodels.iv.covariance.ClusteredCovariance(x: ndarray, y: ndarray, z: ndarray, params: ndarray, clusters: ndarray | None = None, debiased: bool = False, kappa: int | float = 1)[source]

Covariance estimation for clustered data

Parameters:
x: ndarray

Model regressors (nobs by nvar)

y: ndarray

Series ,modeled (nobs by 1)

z: ndarray

Instruments used for endogenous regressors (nobs by ninstr)

params: ndarray

Estimated model parameters (nvar by 1)

debiased: bool = False

Flag indicating whether to use a small-sample adjustment

clusters: ndarray | None = None

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

kappa: int | float = 1

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.

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.