There is a major debate over whether or not Pharaoh hardened himself or whether God hardened him. I think if you just read the Bible plainly it seems pretty obvious,
Exodus 3:19-20, "But I know that the king of Egypt will not permit you to go, except under compulsion. So I will stretch out my hand and strike Egypt with all of my miracles which I shall do in the midst of it; and after that he will let you go."
4:21, "The Lord said to Moses, 'When you go back to Egypt see that you perform before Pharaoh all the wonders which I have put in your power; but I will harden his heart so that he will not let you go."
6:1, "Then the Lord said to Moses, 'Now you shall see what I will do to Pharaoh; for under compulsion he will let them go, and under compulsion he will drive them out his land.'"
7:3-5, "But I will harden Pharaoh's heart that I may multiply My signs and My wonders in the land of Egypt. When Pharaoh does not listen to you, then I will lay My hand on Egypt and bring out My hosts, My people the sons Israel, from the land of Egypt by great judgments. The Egyptians shall know that I am the Lord, when I stretch out My hand on Egypt and bring out the sons of Israel from their midst."
7: 13, "Yet Pharaoh's heart was hardened, and he did not listen to them, as the Lord had said."
7:22, "[A]nd Pharaoh's heart was hardened, and he did not listen to them, as the Lord had said."
8:15, "But when Pharaoh saw that there was relief, he hardened his heart and did not listen to them, as the Lord had said."
8:19, "But Pharaoh's heart was hardened, and he did not listen to them, as the Lord had said."
8:32, "But Pharaoh hardened his heart this time also, and he did not let the people go."
9:7, "Pharaoh sent, and behold, there was not even one of the livestock of Israel dead. But the heart of Pharaoh was hardened, and he did not let the people go."
9:12, "And the Lord hardened Pharaoh's heart, and he did not listen to them, just as the Lord had spoken to Moses."
9:16, "But, indeed, for this reason I have allowed you to remain, in order to show you my power and in order to proclaim My name through all the earth."
9:34 - 10:1, "But when Pharaoh saw that the rain and the hail and the thunder had ceased, he sinned again and hardened his heart, he and his servants. Pharaoh's heart was hardened, and he did not let the sons of Israel go, just as the Lord had spoken through Moses. Then the Lord said to Moses, "Go to Pharaoh, for I have hardened his heart and the heart of his servants, that I may perform these signs of mine among them."
10:20, "But the Lord hardened Pharaoh's heart, and he did not let the sons of Israel go."
10:27, "But the Lord hardened Pharaoh's heart, and he was not willing to let them go."
11:9-10, "Then the Lord said to Moses, 'Pharaoh will not listen to you, so that My wonders will be multiplied in the land of Egypt.' Moses and Aaron performed all these wonders before Pharaoh; yet the Lord hardened Pharaoh's heart, and he did not let the son's of Israel go out of his land."
14:4-5, "Thus I will harden Pharaoh's heart, and he will chase after them; and I will be honored through Pharaoh and all his army, and the Egyptians will know that I am the Lord.' And they did so. When the king of Egypt was told that the people had fled, Pharaoh and his servants had a change of heart toward the people, and they said, 'What is this we have done, that we have let Israel go from serving us?'"
14:8, "The Lord hardened the heart of Pharaoh, king of Egypt, and he chased after the sons of Israel as the sons of Israel were going out boldly."
14:17-18, "But as for Me, behold, I will harden the hearts of the Egyptians so that they will go in after them; and I will be honored through Pharaoh and all his army, through his chariots and his horsemen. The the Egyptians will know that I am the Lord, when I am honored through Pharaoh, through his chariots and his horsemen."
From the get-go, from 3:19, 4:21, 6:1, and 7:3-5, God made it plain that He was the one doing the hardening and that He would be the one making Pharaoh do stuff under compulsion. There really is no way around it, every phrase that says that Pharaoh "hardened his heart," is governed by the opening of the book. God told Moses he would harden Pharaoh's heart and that Pharaoh would let them leave only under compulsion before Moses ever left Midian.
Indeed, 9:34 - 10:1 is of greatest importance in understanding this. Who hardened whom? While it says that Pharaoh and his servants hardened their own hearts, it promptly responds, "Just as the Lord had spoken through Moses!" When did the Lord speak through Moses? Oh that's right, back in 3:19, 4:21, 6:1, and 7:3-5. Not only this but then the Lord claims responsibility for the same hardening that Moses attributes to Pharaoh only a verse earlier! For what purpose? "That I may perform My signs among them."
From first to last, the sovereign hand of God is wielded for one purpose and one purpose only, the glory of God. God hardened Pharaoh so that the nation of Israel and the nation of Egypt would not be in doubt as to who God was and is and so that those respective nations would throw themselves prostrate before Him in awe and worship.
Thus, the sovereignty of God in hardening Pharaoh's heart is eminently practical because it brings to a deep heart knowledge of God's greatness and His majesty and our smallness and depravity. It shows how little we can control anything and how little and weak and non-existent our so-called "will" is.
According to Exodus, this should lead to only one thing: Worship and adoration of the Almighty.
Indeed when all was said and done, Moses could only say in Exodus 15:11-13, "Who is like you among the gods, O Lord? Who is like You, majestic in holiness, awesome in praises, working wonders? You stretched out your right hand, the earth swallowed them. In your lovingkindness you have led the people whom you have redeemed; in your strength you have guided them to your holy habitation."
Therefore, the purpose of the sovereign working of God in both believers and unbelievers, in working salvation and in damning to hell, in hardening and in softening hearts to believe and to work, in keeping all of Israel's livestock and in killing all of Egypt's livestock, in killing all the Egyptian firstborn and keeping all the Israelite firstborn, in leading Israel through the Red Sea safely and in destroying Pharaoh and his army completely in the Red Sea, indeed, in controlling both good and evil causes, is to the magnification of His majesty and the glorification of His greatness.
If our response be anything but worship it is a wrong response. The sovereignty of God in the power to harden and soften hearts is a terrifyingly majestic truth and it demands that we bow low to the King of the universe.
Would you do this? May I plead with you to bow to the almighty, soverign, ordaining, hardening, softening, merciful, wrathful, loving, prescient, ominpotent God of the universe rather than rebelling and saying such an untruth as, "God permitted Pharaoh to harden his heart." This is unbiblical and, dare I say, contrary to the whole point of Exodus 1-15.
God hardened Pharaoh so that you and I would worship. So let me plead with you, please worship this all-controlling and wonderful God!
Soli Deo Gloria
R.D. Thompson