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The fruit he wanted to see produced was not new conversions. Philippians 4:17, where Paul instructs a congregation to which he felt especially close, helps to explain what the apostle meant: "Not that I seek the gift, but I seek the fruit that abounds to your account." In writing to an existing congregation of converted people, he wanted them to exhibit the fruit of righteousness by making use of faith in God's Word (the gospel). They could do this by yielding in obedience to God's instruction through the power and guidance of His Spirit in them.
As a shepherd or pastor, he claims the fruit would also be his, since it would accrue in them as a result of his teaching them the gospel in greater detail. The teaching in Romans exemplifies the detail of the messages he would have given orally had he been there. The good works that they produced by making use of God's Word would also accrue to him as the fruits of his labors for them. When students do well, their success is the fruit of a teacher's labors.
Conversely, Philippians 4:17 explains that Paul is not being self-centered in this. He yearns that they produce fruit through good works so they can receive the benefits. The fruit accrues to their accounts. Thus, producing good fruit requires sound instruction from a qualified teacher (Acts 8:30-31), the Word of God, the Holy Spirit, a believing and receptive mind, and applying the instruction.
John W. Ritenbaugh
The Fruit of the Spirit