Longenecker and Still have stimulating section on the “righteousness of God” in Romans (Thinking through Paul, 174-7). Prior to the Reformation, the phrase referred to the justice of God and his righteous judgment of sin. Think of the Renaissance paintings depicting God as a fearsome judge presiding over the judgment of sinners.
This emphasis led to the unfortunate result of anti-Judaism in biblical studies. First-century Jews become proto-Pelagians and Paul is similar to Martin Luther bashing the Roman church. Judaism was often described as the antithesis of Paul’s (Gentile) Christianity. Paul’s theology developed out of Paul’s personal struggle against Judaism. While this is very preachable, it may not accurately describe Paul’s thinking with respect to the righteousness of God and how that righteousness is applied to the sinner.
Ernst Käsemann argued the “righteousness of God” refers to God’s sovereign activity over all of creation (TTP, 175). More than only saving individual sinners, the righteousness of God that is being revealed in Romans 1:17 is a redemption of all creation. It is not simply that God imputes righteousness to the believer, but that God is ultimately faithful to his promise to redeem creation. This coheres well with the narrative shape of Pauline theology, according to Longenencker and still (176). Just as God revealed his righteousness by remembering his covenant and redeeming Israel in the past (Ps 98:1-3), so he now reveals his righteousness buy redeeming all of creation through Christ Jesus.
In the Hebrew Bible, this meant God kept his promises to bless Abraham’s children even though there were unfaithful. He kept his promise to Israel even though they were unfaithful to the Law. In the present age, God is still faithful in keeping his promise to redeem people from slavery to sin despite their longstanding rebellion against God. This faithfulness of God is sometimes described as “steadfast love” (חֶסֶד, Ps 98:3, for example).
Is this a better way of understanding the “righteousness of God”? It seems to resonate with what Paul says in the rest of Romans, but does it stray too far from “personal salvation”? Perhaps there is a danger in over-emphasizing the action of God for all of creation and missing the “call to salvation” the Gospel offers to individual sinners.
It is also possible Evangelical Christianity has so over-emphasized personal righteousness in salvation that we have missed Paul’s point: it is God’s righteousness that is demonstrated in his offer of salvation. Certainly Paul is talking about the problem of our sin, but the emphasis is on the sovereign God who solved that problem because he is a righteous judge.