Is that just another big word for sesquipedalians to throw around? Be that as it may, the term lends itself to unraveling an apparent theological knot that has tied up the minds of believers again and again. But first, what does coefficiency mean?
To say two things are co-efficient is to say they share in effecting a result. They co-operate. Both go together to cause something else. Both of your feet are coefficient to your walking. But we would not say the same about the shoes you wear while walking. Shoes co-incide (occur at the same time) with walking, but do not co-effect walking.
Which brings us to that apparent knot that must be unravelled as we consider the words of the apostles Paul and James when it comes to faith and works, viz;
"For we hold that one is justified by faith apart from works of the law." (Romans 3:28)
"You see that a person is justified by works and not by faith alone." (James 2:24)
WHOA! Bible contradiction? Does Scripture tell is in one place that faith and works are NOT coefficient, and in another passage tell us that they ARE? Not at all. The two passages are in fact complementary...they go together. The two inspired apostles look at the relationship of faith and works from two perspectives.
The whole counsel of God in Scripture assures us that ultimately, a sinner is justified before God by His GRACE. Saving faith, itself a gift of God, is "downstream" of sovereign grace. Works are the fruit and evidence of true faith and inseparable from it. The ones to whom God gives the gift of genuine faith lay hold of His grace alone for justification, and go on to do works as a result of their new sonship relationship with God.
"For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them." (Ephesians 2:10) So faith itself is God's gift and the works that flow from true faith are also God's gifts, prepared in advance for the faithful!
As another writer put it, "Paul severs works from justification, but not from true faith. James joins works to true faith, but not to justification." The saved are saved by grace through faith alone, but not through a faith that IS alone.
Thus the knot is untied and the Christian is free from the fear that his works must be coefficient with faith for his justification. Rather, being justified by grace through faith, he walks in that faith, doing the good works which God in grace has prepared for him. We might say that works are the "gift shoes" which coincide with the gift of faith as the Christian walks onward in the life of discipleship by grace.