# linearmodels.iv.covariance.ClusteredCovariance¶

class linearmodels.iv.covariance.ClusteredCovariance(x: ndarray, y: ndarray, z: ndarray, clusters: = None, debiased: bool = False, kappa: = 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: = None

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

kappa: = 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.