Consider an ergodic non-singular action \(\Gamma \curvearrowright B\) of a countable group on a probability space. The type of this action codes the asymptotic range of the Radon–Nikodym derivative, also called the ratio set. If \(\Gamma \curvearrowright X\) is a pmp (probability-measure-preserving) action, then the ratio set of the product action \(\Gamma \curvearrowright B\times X\) is contained in the ratio set of \(\Gamma \curvearrowright B\). So we define the stable ratio set of \(\Gamma \curvearrowright B\) to be the intersection over all pmp actions \(\Gamma \curvearrowright X\) of the ratio sets of \(\Gamma \curvearrowright B\times X\). By analogy, there is a notion of stable type which codes the stable ratio set of \(\Gamma \curvearrowright B\). This concept is crucially important for the identification of the limit in pointwise ergodic theorems established by the author and Amos Nevo. Here, we establish a general criteria for a nonsingular action of a countable group on a probability space to have stable type \(III_\lambda \) for some \(\lambda >0\). This is applied to show that the action of a non-elementary Gromov hyperbolic group on its boundary with respect to a quasi-conformal measure is not type \(III_0\) and, if it is weakly mixing, then it is not stable type \(III_0\).