The difficulty is related to total hashing power (e.g. electricity if most of the miners have access to similar mining technology), and daily electricity cost won't be higher than daily coin output value, so there is some correlation. The question is: which is the cause, difficulty or price?
As you say, one cannot say anything about causality. Sorry for the formatting but it is late now. I might look more into this later.I suspect there is a bit of both affecting each other, among other influences, but between the two mentioned it seems it would moreso be that prices lead to an acceleration of network-hash-rate.
Here's an idea for you:
Plot the ROI's of the most efficient (GigaHash/$spent) hardware (at any one time) over time (CPU's, GPU, FPGA's to ASIC's). I'll guess that you will likely see a cycle of up and down with a average around 10 months ROI that is causing people to react. For example, if ROI's go below 10 months (b/c of increased bitcoin value) it will attract more miners and accelerate hash rate. When ROI's become too long, then people will find other ways to invest their money beside mining or apart from bitcoin. There's probably a balance point of ROI's, but I don't think it will ever stabilize. Assume, for example, ROI's stabilized to 10 months. Prices stabilized..etc... then outside demand will be the only driving mechanism.
Also, what miners are expecting is important. Do they just want to mine and sell on a regular basis? or Do they largely prefer to hold, maybe until bitcoin reaches some (super?) high target?
