An interleukin receptor subunit with specificity for interleukin-13. It dimerizes with the interleukin-4 receptor alpha subunit to form the TYPE II INTERLEUKIN-4 RECEPTOR which has specificity for both INTERLEUKIN-4 and interleukin-13. Signaling of this receptor subunit occurs through the interaction of its cytoplasmic domain with janus kinases such as the tyk2 kinase.