In the latest issue of the International Journal of Systematic Theology, the redoubtable and hyper-productive Matthew Levering probes Augustine’s arguments (in de Trinitate) for concluding that the Spirit is “love” and “gift.”
As Levering points out, the identifications are not straightforwardly asserted anywhere in Scripture, yet Augustine makes a Scriptural case. The description of the Spirit as “gift” is more overtly taught in the New Testament, and Augustine links this with “love” by saying that the gift that God gives is the gift of love. Hence, the Spirit who is gift is also the Spirit who is love.
Augustine recognizes that naming the Spirit “gift” runs the risk of depersonalizing the Spirit, and so he “emphasizes in Book V that the Spirit is for us as an active origin or divine giver of gifts. Otherwise it would have been impossible for Paul to speak of ‘one and the same Spirit, who apportions to each one individually as he wills’” (139).
Augustine is also aware that the New Testament speaks of the Spirit as a gift insofar as He is a gift to us. But Augustine is willing to extrapolate from this economic work of the Spirit to a conclusion about the immanent Trinity. Behind this Levering discerns a view of Scripture that is quite different from that of modern critical scholarship. “For Augustine, Scripture is not a mere set of ancient texts whose meaning can be traced by reading each text individually. Instead, the triune God inspired Scripture in order to teach us about himself, so that we can know him rightly and thereby come to love him more and more” (141). Since Scripture is given to reveal God to us, texts that speak of the Spirit as love and gift in the economy “can also be expected to teach us about the procession of the Holy Spirit” (141-2).
(Levering, “The Holy Spirit in the Trinitarian Communion: ‘Love’ and ‘Gift’?” IJST 16:2  126-42.)