Dear STATA community,

I have some questions regarding my analysis for my DID estimation. I am looking at the effect of the EU-ETS (Emissions trading system) on carbon emssions from Norwegian industrial activity. I have been able to collect data for 5 treatment industries (with there being possibility to collect for 7 in total) and 10 control industries. This gives me a total of about 450 observations. Sectorid stands for the 15 different industries. GDP_Abroad stands for GDP from the US. CO2GDP stands for CO2 divided by GDP, ie CO2/GDP. I have the results for about 4 dfferent regressions with the first being without any logs or other variable transformations, second being with logCO2 whilst the other being the same as before, third being logCO2, logGDP and logGDP_Abroad, and fourth being logCO2GDP and logGDP_Abroad.
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If I understand correctly, from the results that I have gotten above none of my results from the 4 regressions are significant. Meaning the coefficients cannot be really used to make any statistical inferences.
Secondly, If some of the results (like the one that is log - transformed) is significant, then the interpretation of the coefficient is that applying a EU-ETS would actually lead to an increase in CO2 in percentage or units? (whilst I was assuming a decrease in CO2 emissions would occur as it is supposed to function as a emission reducing instrument rather than the other way around)
Lastly, the parallel assumption is the main important assumption that needs to be satisfied when running a DID. I got the following values for the 4 regressions on the parallel test, 0.00, 0.77, 2.27, and 2.29. Looking at these four values I am assuming that my parallel assumption for all 4 regressions are satisfied, ie not to reject the null hypothesis of Linear trends are parallel.

Thanks for a constructive feedback