Hierarchical κ-statistics are used to measure the extent to which two raters agree between themselves when the rating scale is ordinal. If the agreement is not perfect, hierarchical κ-statistics are useful to measure the agreement at several levels. In this paper a model-based method is proposed to estimate the hierarchical κ. It has been noted before that the estimates obtained have smaller mean-squared error than the existing estimates in finite samples. In this paper we show that asymptotically also the model-based estimates are more precise in the sense of having smaller variances. Another advantage of the model-based method is that it can be extended easily to any weighting scheme and tables of any dimensions in both theory and practice.