As I mentioned in this post, I wanted to give an example of what it looks like for theology to be lived out. I selected imputation for two reasons, one convenient in that I came across it in my study of Philemon, and the other intentional in that I wanted to pick a doctrine that seems esoteric.
First let's begin by explaining imputation. The main idea of the doctrine of imputation claims that an exchange took place between us and Christ. When Jesus died on the cross, he bore the wrath of God that we deserve so that if we have faith in him we no longer have to face God's wrath. Here's where imputation comes in: our sinfulness was credited to Jesus as if he had sinned ('God made him who had no sin to be sin for us' - 2 Cor. 5:21a TNIV). Our sin was counted as if it was Jesus sin which, since Jesus paid the penalty for our sins means that our sins are wiped away. The imputation part of this, again, is our sins being credited to Jesus. This is not enough for us to be accepted before God, though. All we are at this point is morally neutral, thus another imputation must take place. Jesus moral righteousness is credited to our accounts, and now we see all of 2 Cor. 5:21, 'God made him who had no sin to be sin for us, so that in him we might become the righteousness of God' (TNIV). Through our union with Christ in his death and resurrection, his righteousness is counted as our righteousness, thus when God looks at us he sees the perfect record of his Son. In summary, the doctrine of imputation teaches that our sinfulness was credited to Jesus and his righteousness was credited to us, which allows us to be reconciled to God.
What does that look like? I would argue that Philemon 17-19 gives us a picture of how Paul lived out imputation: "17 So if you consider me a partner, welcome him as you would welcome me. 18 If he has done you any wrong or owes you anything, charge it to me 19 I, Paul, am writing this with my own hand. I will pay it back—not to mention that you owe me your very self." (TNIV).
Paul's goal was to reconcile Philemon and Onesimus. There were hurdles that had to be overcome before this could happen. Onesimus had fled Philemon and thus wronged him by being absent for at least a few months and thereby incurring the cost of lost labor (and perhaps the hire or purchase of additional slaves). It's possible too that Onesimus had stolen from Philemon to finance his journey to Rome. Thus Onesimus has a substantial debt that he owes Philemon. This is an obstacle to their reconciliation. That does not stop Paul, though. In verses 18 and 19 we see Paul, in a legally binding manner, absorb the debt that Onesimus owes Paul. He is willing, like Christ, to pay the penalty on behalf of another. Don't forget that Paul was in prison at the time, so if Philemon asked Paul for payment, it would be very difficult and very costly to pay.
On the flip side, Paul knows that he has a strong relationship with Philemon. He knows that Philemon loves him and would be overjoyed to see Paul (notice in vs. 22 Paul asks Philemon to prepare a guest room for him). Paul had been of great benefit to Philemon and was his father in the faith. What Paul does in verse 17 is ask that Philemon see Onesimus as he would Paul. Thus Paul's positive record is being imputed to Onesimus.
One big thing that the doctrine of imputation teaches us is of the costliness of Christ's sacrifice for us to reconcile us to God. We too, like Paul, are ministers of reconciliation (2 Cor. 5:19-20). Also, like Paul, our ministry of reconciliation is not solely about reconciling others to God (though this is primary). We are to work for the reconciliation of one to another even if it's at great cost to ourselves, especially when division exists between fellow believers. We must be willing to absorb penalty and pain and use our positive influence to repair damaged relationships.