The work of redemption and reconciliation which is at the heart of the covenant of grace is as much the work of the Spirit as it is of the Son and the Father. Wherever we cut the cake we find the same harmony, the same unity of purpose, and the same interpersonal involvement. Father, Son and Spirit each had their equally important role to play in creation, and each had their equally important role to play in redemption. Jesus was conceived by the Spirit (Matt 1.18,20); during his ministry he was empowered by the Spirit (Luke 4.1,18; Matt 12.28); through the Spirit he offered himself as a sacrifice without spot to God (Heb 9.14); by the Spirit he was raised from the dead (Rom 8.11).And it is only in so far as the preaching of the good news of Christ is empowered by the Spirit that it is effective in the minds and hearts of the hearers (1 Cor2.4; 1 Thess1.5).
We have already distinguished between the primary, objective work of Christ for the believer and the secondary, subjective work of Christ in the believer. This secondary, subjective work is the particular responsibility of the Spirit. It is the Spirit who applies the work of Christ so that it becomes real and relevant to the individual. As Bromiley says, "Baptism is not just any baptism; it is my baptism. It is my own entry by the word and Spirit into Christ's victorious work. It is my own identification with him, so that I can now say with the apostle: 'He loved me and gave himself for me.' (Gal 2.20)" Children of Promise Yet even here the subjective depends on the objective. It is only through the regenerative work of God the Holy Spirit that we are able to enjoy the benefits of Christ's death, and it is this regenerative work of the Spirit that is signified in water baptism.
One last thing. If it is the Father who is the initiator of the covenant and the Son who is the mediator of the covenant, it is the Spirit who seals God's people as his own within the covenant (2 Cor 2.22; Eph 1.13f). All this is contained within the Bible's understanding of baptism.