Windfall Profits Tax is a (Weak) Pigovian Tax

Mankiw argues that Obama's Windfall Profits Tax is not Pigovian. I disagree. It is only not pigovian in a completely hypothetical world where world supply of oil can exactly offset the decrease in domestic supply brought about by the increased domestic burden placed via the tax, or, in a world where changes in inputs or business structure due to the tax increase have no effect on pricing.

As I mentioned here, the windfall tax is different than a consumption tax largely, as Mankiw points out, it is more distortionary. But, provided world supply is constrained to some degree greater than zero, then world supply of oil will fall by some percentage that domestic supply falls by as the overall cost of production rises, thereby raising the price of oil and reducing consumption - sounds pretty pigovian to me - albeit a weak one as a windfall tax is not likely to increase price dramatically as world supply would surely partially compensate. Mankiw's own cite - Josh Barro - makes this very point in his last sentence of his post:
"So there's your windfall profits tax in a nutshell: reduced domestic production, increased dependence on foreign oil, and pump prices either unchanged (best case) or higher (worst case)."

It is true that a windfall profits tax could distort the labor/capital tradeoff, but even that would presumably increase the costs of production and the price of gas at the pump as any tradeoff change would be less than optimal due to a tax on domestic profit.

So, I fail to see how a windfall profits tax can be labeled NOT pigovian. It seems more accurate to label it as LESS pigovian than the proposed consumption tax would be. There would have to be some pretty extreme assumptions made to call a windfall profits tax completely 100% not pigovian.