Understanding of the phrase “God’s purpose according to His choice” is critical to a proper understanding of Romans 9:6-13. Regarding this phrase, there are two questions that must be addressed.
But it is not as though the word of God has failed. For they are not all Israel who are descended from Israel; nor are they all children because they are Abraham’s descendants, but: “through Isaac your descendants will be named.” That is, it is not the children of the flesh who are children of God, but the children of the promise are regarded as descendants. For this is the word of promise: “At this time I will come, and Sarah shall have a son.” And not only this, but there was Rebekah also, when she had conceived twins by one man, our father Isaac; for though the twins were not yet born and had not done anything good or bad, so that God’s purpose according to His choice would stand, not because of works but because of Him who calls, it was said to her, “The older will serve the younger.” Just as it is written, “Jacob I loved, but Esau I hated.”
First, what is meant by “God’s purpose?” A close reading of verses 11-13 will reveal that in the example of Jacob and Esau God purposed to freely elect apart from man’s actions. Paul reminds his readers that although they “were not yet born and had not done anything good or bad… it was said to her, ‘The older will serve the younger.'” The intention of this election of Jacob over Esau was “that God’s purpose according to His choice would stand, not because of works but because of Him who calls….” God used this election of Jacob over Esau to uphold His purpose, a purpose which Piper views as being defined by the phrase according to election. Thus, “God’s purpose [is] an electing purpose, a purpose to be one who selects on the basis described in 9:11 and 9:12ab, namely freely, with no constraints from or ground in human distinctive. In short God’s purpose is to be free from all human influences in the election he performs.”
The ἵνα clause + subjunctive should probably be seen as a purpose clause, however it could also be seen as a result clause; the difference between the two is not substantial. Piper, The Justification of God: an Exegetical and Theological Study of Romans 9:1-23, 53.