Hierarchical Priors - problems when hierarchical variance drops

In the docs here: 1.10 Hierarchical priors | Stan User’s Guide

It explains that as the hierarchical variance approaches zero, you can have issues. It recommends the following:

The approach recommended by Chung et al. (2013) is to use a gamma distribution as a prior, such as


Is this a typo? It wants to recommend a prior on τ not σ right?

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