Does God cause sin?

Does God cause sin?  Arminians say no, God permits sin.  Calvinists say no, God ordains sin.  What do you think?

21 And the Lord said to Moses, “When you go back to Egypt, see that you do before Pharaoh all the miracles that I have put in your power. But I will harden his heart, so that he will not let the people go.   Exodus 4:21

2 You shall speak all that I command you, and your brother Aaron shall tell Pharaoh to let the people of Israel go out of his land. 3 But I will harden Pharaoh's heart, and though I multiply my signs and wonders in the land of Egypt, 4 Pharaoh will not listen to you. Then I will lay my hand on Egypt and bring my hosts, my people the children of Israel, out of the land of Egypt by great acts of judgment. 5 The Egyptians shall know that I am the Lord, when I stretch out my hand against Egypt and bring out the people of Israel from among them.”  Exodus 7:2-5

Let's proceed inductively.

Did God harden Pharaoh's heart?

Was it because of Pharaoh’s hardened heart that he refused to obey God and sinned by not letting the Israelites go?

So we could say God did not cause Pharaoh to sin but rather Pharaoh’s hardened heart caused him to sin.  But then we have to ask did God cause Pharaoh’s hardened heart? Obviously based on Exodus 4:21, God says, "I will harden his heart".  So God did in fact cause the hardened heart.

Why did God cause the hardened heart?  Exodus 4:21 says "so he will not let the people go."  Exodus 7:5 adds, "The Egyptians shall know that I am the Lord."  Paul says in Romans 9:17,

"17 For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.”

So if God caused the hardened heart which caused the sin then perhaps we would be correct to say that sin can occur as a result of something God causes. So God does not cause the sin but rather causes the circumstances which He in his omniscience and perfect wisdom knows will cause sin through which his purposes will be accomplished.