The ancient Jew thought in terms of first cause. When there is a chain of causes and consequences they thought and expressed the first one. It would go like this; God gave all human's free will and Pharaoh was a human. Free will allows Pharaoh to have choices. Pharaoh chose to harden his heart and therefore God hardened Pharaoh's heart.
It is impossible to understand the Old Testament without understanding how the writers and readers thought and expressed themselves. The New Testament in the main follows Greco-Roman logic and thinking. When we find inconsistancies between the OT and NT, most often it is because we don't understand the culture, thought patterns and circumstances of the two.