How to isolate price effect in time series? Here is what I have:


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*Excel

*Yearly energy prices by state from 2002 (generally increasing, generally peaked a couple of years ago)

*Yearly energy consumption by state by industry from 2008 (about 700 state/industry combinations; various patterns, from clear trends to sawtooth)


I want to get a rough, quick and dirty estimate of in which state-industry dyads are increasing energy prices likely to be causing a reduction in energy demand since 2015. 
However, there are a few confounding issues, including that the GFC around 2008 would depress energy use, energy consumption is driven by many things other than price, and that many industries have been getting more energy efficient over time. Also, since about 2015 the average energy supply contract duration has shrunk from 3-5 years to 6-12 months. This means that I would expect to see a sharper drop in energy use since 2015. How can I check for this?
I'm not sure how to control for these issues with what I have.
Can I just regress energy use against price for each state-industry dyad and check the p-value for the slope? Or is there a better way to do this?
 A: Question: "Can I just regress energy use against price for each state-industry dyad and check the p-value for the slope? Or is there a better way to do this?
ANSWER: Only if your observations are independent in time AND there are no anomalies or level shifts or trend changes and there is a constant error process over time. http://autobox.com/dave/regvsbox.pdf (which I authored) discusses issues/differences/opportunities/pitfalls when dealing with time series that your suggested regression solution may be ignoring.
If there are time series "complications" and they have been incorporated you can use the t value/p value for the price variable
A: Yes you can; only after understanding the types of variables energy use and price are that you can choose an appropriate model that best describe them.
A: The typical answer here is that if you want to control for these factors, you have to find a way to measure them, and include them in the regression. So that you can estimate the conditional effect of price (conditioned on the others being constant) by virtue of the regression model. 
If you want a "quick and dirty" way, I suggest the best is to get quick and dirty estimates of the confounders - instead of ignoring them.  
