Cluster-Robust Covariance Estimators

In many settings, observations may be grouped into different groups or “clusters” where errors are correlated for observations in the same cluster and uncorrelated for observations in different clusters. EViews 10 offers support for consistent estimation of coefficient covariances that are robust to either one and two-way clustering.

 

As with the HC estimators, EViews supports a class of cluster-robust covariance estimators, with each estimator differing on the weights it gives to observations in the cluster.

 

The weighting of each estimator is as follows:

 

$$\begin{array}{c}\text{Method}\end{array}$$	$$\begin{array}{c}\text{Weight}\end{array}$$
$$\begin{array}{cc}\text{CR0 – Ordinary}& 1\end{array}$$	1
$$\begin{array}{c}\text{CR1 – finite sample corrected (default)}\end{array}$$	$$\begin{array}{c}\sqrt{\frac{G}{(G-1)}\cdot \frac{(T-1)}{(T-k)}}\end{array}$$
$$\begin{array}{c}\text{CR2 – bias corrected}\end{array}$$	$$\begin{array}{c}\mathrm{(1}-h_t{)}^{-1/2}\end{array}$$
$$\begin{array}{c}\text{CR3 – pseudo-jacknife}\end{array}$$	$$\begin{array}{c}(1-h_t{)}^{-1}\end{array}$$
$$\begin{array}{cc}\text{CR4 – relative leverage}& \end{array}$$	$$\begin{array}{c}(1-h_t{)}^{-{\delta }_t/2}\end{array}$$
$$\begin{array}{c}\text{CR4m}\end{array}$$	$$\begin{array}{c}(1-h_t{)}^{-{\gamma }_t/2}\end{array}$$
$$\begin{array}{c}\text{CR5}\end{array}$$	$$\begin{array}{c}(1-h_t{)}^{-{\delta }_t/4}\end{array}$$
$$\begin{array}{c}\text{User – user specified}\end{array}$$	$$\begin{array}{c}\text{arbitrary}\end{array}$$

 

where $h_t=X_t^{\top }{\left({}^{}X\right)}^{-1}{X}_t$ are the diagonal elements of the familiar “hat matrix” $H=X^{\top }{\left({}^{}X\right)}^{-1}X$, ${\delta }_t$ and ${\gamma }_t$ are discount factors, and $G$ is the number of clusters.