  We investigate the joint asymptotic behavior of so-called blocks estimator of
the extremal index, that determines the mean length of clusters of extremes,
based on the exceedances over different thresholds. Due to the large bias of
these estimators, the resulting estimates are usually very sensitive to the
choice of the threshold and thus difficult to interpret. We propose and examine
a bias correction that asymptotically removes the leading bias term while the
rate of convergence of the random error is preserved.
