There have been claims that Bitcoin price and difficulty correspond. Is there empirical data to support or refute this?
This leads to the conclusion that price drives difficulty. A drop in price caused a drop in difficulty. I have noticed this same correlation on another occasion; about two months ago.
Also, the reverse is probably true. When the price soared to $30+; the network hash rate accelerated greatly. The higher prices clearly attracted miners.
This relationship can be seen visually, though it is a rough correlation. In the all time chart (scroll down) you can see the orange being the price at Mt. Gox, and the grey line that steps up and down being the difficulty.
Summary: AFTER the price moves, the difficulty follow the same direction, ... lagging two to five weeks roughly: - http://tvori.info/bitcoin/charts
The green line shows profitability, which is not part of your question but is the most important line in that chart so I wanted to point that out.
Incidentally, following the traders on the #bitcoin-otc marketplace gives the anecdotal evidence that
The purpose of the difficulty is to ensure a blockchain solution is produced roughly every ten minutes. If there is a lot of hashing power available then solutions will be found quickly which causes a correction to make it harder, or conversely to make it easier.
So the nub of the question is what causes variation in the hashing power? The short answer is the efficiency of solving the problem. This introduces other aspects:
Assuming that most miners are in it for the money rather than just being enthusiasts, then the primary concern is profit margin. So long as a miner can turn a profit that exceeds other available investments then he is rational to continue mining. He then faces the problem of maximising his profit margin above the break even point.
Once way is to find and exploit a super-efficient way of solving the hashing problem just a little ahead of other miners then his operating costs are reduced without unduly affecting the difficulty level.
Another is to reduce operating costs, perhaps by taking advantage of free electricity. He may even enjoy the side effect of heating his home during cold winter months, this reducing his operating costs further.
This would mean that hash rate would be invariant against mild fluctuations in the price of a bitcoin.
So, in short, it is individual profit margin to miners that drives the hash rate, not the naked price of a bitcoin.
Here you go!
Click the tab at the bottom Difficulty Versus Price for a chart view.
As-of Jul 4, 2012 here's those charts: