Explanatory and explained variables with opposite time trends

[Maria Roszkowska-Menkes]

Dear All!


I am conducting a cross-country study exploring the relationship between ESG disclosure and country and corporate level governance. I use random slope mixed-effects ML regression model. My data set consists of 52,022 observations over 10 year time period (2011-2020) from 6237 firms and 66 countries.

ESG disclosure (esg_dis - explained variable) has a clear positive trend. One of the main explanatory variables, level of civil liberties (cl) in a country has been decreasing over the analyzed time period.

The relationship I get from my analysis is negative. Although this can be explained by the theory, most of the previous research shows positive relationship.

I did include year dummies in my model, but is it enough to control for these time trends?

mixed esg_dis cl esg_bonus brd_size ind_dir wmn_pct ceo_duality roa ln_assets debt_equity crss_lst unemployment i.common mandatory_esg i.year i.ind || country: cl || id:

How can I control for the time trend in such situation?

Any advice would be highly appreciated
Many thanks!

[Clyde Schechter]

Well, your model, by incorporating i.year, already accounts for the time trend in ESG disclosure, whatever that is! Please, this being a multidisciplinary forum, do not use abbreviations or terms that would not be recognized by everyone with a college education.

If you want to make the time trend more explicit in the output, you can include a c.year term in addition to i.year. If you do that, c.year must precede i.year in the list of variables; otherwise Stata will drop it due to colinearity with the i.year indicators. And actually, if you have hopes of using the -margins- command later, rather than using c.year you should make a new variable that equals it, and then incorporate that as the time trend variable (with c. prefixed, of course). -margins- will not tolerate the same variable being used with both c. and i. in an estimation. But doing this isn't going to change the estimation of the cl effect. That's already baked in with the i.year term. Remember, if you add c.year to the model, that the i.year coefficients will represent deviations around the linear trend line, not shocks from the base year. Also, if you do this, due to colinearity introduced, Stata will omit an additional year indicator--so don't be surprised or concerned about that.

It is curious to have a theory that explains your negative relationship when most previous studies have shown positive relationships. Can you, in a principled way, identify flaws in the design or analysis of those other studies, or some reason why the theory would not apply to them?

In any case, it appears you are uncomfortable with your finding of a negative slope. It is always a good idea to review the design and analysis plan you made, even when you get the results you were expecting or hoping for. (Some might say especially if you get the results you were expecting or hoping for.) Is your sample a true randomly selected sample of the entities in question? If not, can you convince people that it is, at least, a representative sample in some way? Are your measurements valid? Did your data management introduce errors into the data before you ran your model? Did you bias the analysis by choice of inclusion and exclusion criteria. (For example, excluding an entity that only has at least some minimum number of observations is commonly done, but can easily lead to biased results.) Have you drawn a diagram of the presumed causal relationships among the variables available to you? Have you omitted any important confounders from the analysis? Have you neglected to include important interactions? Have you mistakenly included a variable that lies on the causal path between cl and esg_dis? Have you mistakenly included a collider (a variable that has causal paths leading into it from both cl and esg_dis?) These are just some of the "usual suspects" that one should consider when questioning the validity of an analysis. There may be other considerations that might be obvious to somebody in your discipline as well. I'm guessing you are working in finance or economics, there are many such people in the Forum, and if one sees this post and notices a problem from that perspective, hopefully, that person will post a response, too.

[Jared Greathouse]

I tend to agree with Clyde: I've no idea what ESG disclosure is. The first Google hits on the phrase are murky, and it's unclear what it means in this situation.

Anyways, I'm no economist, and I'm certainly no finance researcher, but my question to you, is what's the goal of this paper? Do you seem to infer causality, or do you seek simple associations? If you do want causality, then our advice on the statistics can only go so far, as you typically need to either be a subject matter expert or have a good working knowledge of the subject to do good causal inference.

This is my opinion, and I know others will disagree with me, but this is sort of why I think theory can be a hindrance to certain areas of scientific practice. People are so caught up on what theory they buy more, which theory or set of theories are the most sensible, or if their results are consistent with theory, that they, in my opinion, neglect the science angle of what they're doing. I think unconsciously, it can prevent people from making perfectly good choices from a design perspective simply because others haven't done it before or theory (as though it's some Holy Text) hasn't commented on it before. Maybe it's sensible for your results to go against previous work- if you've designed your paper well, which I can't comment much on, maybe your results are sensible to... I don't know, scholars of econometrics and corporate finance

[Maria Roszkowska-Menkes]

Dear Clyde and Jared,

thank you for your comments. Forgive me for using the abbreviation - ESG disclosure stands for information on environmental social and governance performance that companies (still mostly stock exchange listed companies and these are included in my sample) provide alongside their financial statements.

I am a management scholar and I’m interested how companies react to changes in the level of civil liberties that I use as a proxy of public scrutiny (yes, I infer causality). Different management theories predict different outcomes. When it comes to previous studies, the most obvious difference is the time period analysed. Most of them analyse data to 2017, my sample includes 2018-2020, which is actually the time when ESG disclosure has exploded worldwide. But my results don’t change if I run the same analysis for shorter period.

Adding c.year was also a solution that I was thinking of, but I used it without i.year. I’ll try again with this approach. Thank you!

I will also go through all of the questions that Clyde posted.

Again, thank you for your help!