Difference in Difference estimation on carbon emissions in STATA 17.

[Ali Burki]

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.

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

[George Ford]

The third model is stat sig at the 5% level and it makes the most sense to me (all logs). Positive sign makes for controversy, which means you're more likely to get published in a good journal '; ).

What is GDP? I'm curious why the time dummy does not eat the GDP variables if they are common to all cross sections.

Might need to bootstrap with only 5 treated units, but that won't likely help with significance levels. (wildboot option).

Check for common trends. If untreated units are falling pre-treatment faster, then the positive sign might be expected.

[George Ford]

Also, with some cap and trade programs, the industries that more easily reduce CO2 emissions sell permits to industries where it is harder (more costly). This could shift emissions to the treated units, even if total emissions decline.

[Ali Burki]

Thanks for the feedback George Ford. I agree with your second post regarding cap and trade programs and why I am experiencing a positive sign on the coefficient. GDP stands for Norwegian GDP for these industries. I will check the bootstrap and common trends option, but what do you think about the parallel trend test values given in the text above? I think the values are low enough that the parallel assumption for the DID analysis is satisfied, meaning I do not have to reject the null hypothesis on parallality of the linear trends

[George Ford]

There are no parallel trends results I see. Parallel trends is assess pre-treatment. You need a dummy = 1 for any treated unit in all time periods. Then inspect visually for starters. -lgraph- is good for that.

[Jared Greathouse]

Ali Burki This is just my opinion, people don't have to agree with me necessarily, but the best way to get around the parallel trends assumption, if possible, is using synthetic controls, since synthetic controls forces your trends to be parallel. But barring that, in DD estimation, you have to be concerned about not just parallel trends, but heterogeneous treatment effects over time. So, you'd likely want to look at recent estimators such as did_multiplegt, did_impute, eventstudyweights, and others that can adjust for this, if you've got the statistical chops/data setup to justify this.

As George Ford says, I would also strongly recommend graphical analysis of PTA, so you and you audience can actually see the trends for themselves.

[Ali Burki]

George Ford. Here is the parallel trends results for the significant model (the one with logs on all three variables ie CO2, GDP and GDP_Abroad).

Jared Greathouse Thanks for the feedback. Will look into these options but as you just mentioned regarding synthetic control designs the heterogeneous treatment also needs to be taken into consideration

[George Ford]

That's cover but close to significant so I'd dig a little deeper. There may be a couple of series that are off. Graph it out, one by one, and see if something shows up. Also, a test may fail to reject because the slope is poorly estimated. And, PT is untestable (ptrends is supportive, not conclusive), so good visual evidence is important.

Another good approach is false treatment. Shift your treatment date up a few years (e.g., 2, 3, 4, 5 years), drop the real treatment period, and see if the DID coefficient is significant.

Is there any evidence or reason to believe that firms shift behavior in response to the legislative effort, prior to its codification?

Synthetic control might work with this sample as you have few cross sections and a uniform treatment date. I've not had much luck with it, but it's popular. There are a lot of questions about how to get the pre-fit, so read up on it.

[Enrique Pinzon (StataCorp)]

Hi Ali,

I would suggest you try -estat trendplots- to obtain some of the graphical inspection that George suggests. For the shifting treatment date plot you can look at the forthcoming Stata Journal article by Clarke and Tapia-Schythe they provide code to produce such graphs.

https://www.damianclarke.net/researc...panelEvent.pdf

[Ali Burki]

George Ford Thanks again for the useful hints and information. I got what I was looking for in this reply of yours.
Enrique Pinzon (StataCorp) Thanks for the feedback. Will look into article and try the graphical plots function in STATA