How do I combine quarterly and yearly data in a regression?

[Anela Kien]

Hello,

I would like to know if it is advised to use a regression where some variables are based on yearly data and some vary between the year (quarter)?
My dependent variable is quarterly data and some of my independetn variables are yearly (e.g. Leverage) and some are quarterly (stock returns).
I could calculate yearly stock returns via aggregating (geometric returns or artithmetric?). But it would not make sense to calculate quarterly Leverage (it is only reported once a year and dividing it by 4 would not make sense as it is a ratio (Debt / Total Assets).

What would your advise be for me? To this date, I just use yearly data as four obervations over a year (every quarter has the same value).
I am using firm and time fixed effects (quarterly) and clustered SE on firm level.

Thank you in advance!

[Clyde Schechter]

To this date, I just use yearly data as four obervations over a year (every quarter has the same value).

That is what I probably would do. One circumstance where I would roll everything up into yearly data is if the outcome variable is yearly (i.e. takes on the same value in every quarter, or is only measured once a year). In that case, the extra variation within year of the independent variables would have no opportunity to exert an influence on the outcome. But if your outcome variable is quarterly, aggregating everything up to yearly is just throwing away useful variation, and, crucially, co-variation, that can make your estimates more precise.

[Anela Kien]

Thank you for your fast response, Clyde!

I would be very happy if I could use the regression as I am till now.
So, you think that there is no problem if my dependent variable is quarterly data and some of the independent variables are yearly and some are quarterly?
In basically all finance papers the researchers use exclusively yearly data (e.g. carbon emissions or leverage etc. which are reported yearly) or everything is monthly (mostly with factor models / using returns like in the CAPM).
I am aware that not everything is correct what is published, but I was concerned about this "problem".
On another post I was advised to use firm + quarter FE and cluster on firm-level but not on time-level (year or quarter), but in that post I did not share the information about this combination of quarterly and yearly data.

Would this still apply in your opinion, at least with the information given by me?

Also how would you explain or write this in a study? I could not find examples when I did my research as this approach seems to be very uncommon.

Best regards,
Anela

[Clyde Schechter]

So, you think that there is no problem if my dependent variable is quarterly data and some of the independent variables are yearly and some are quarterly?

That's not exactly what I meant. What I wrote in #2 is based on my (unstated) assumption that the leverage data being used is annual because quarterly data is not available. It would clearly be better to use quarterly data on everything. I assume the reason you did not do so is because such data either do not exist, or you were unable to obtain them. If they are out there and in your grasp, then it is best that you gather them and use them. But you cannot analyze data that you cannot get. And assuming that the yearly data are the highest frequently available to you for those measures for these firms, my point is that coarsening everything else is less desirable than going with what you have.

Also how would you explain or write this in a study?

I don't think you need to explain this beyond stating that you used the most frequently measured data available for each variable.

On another post I was advised to use firm + quarter FE and cluster on firm-level but not on time-level (year or quarter), but in that post I did not share the information about this combination of quarterly and yearly data.

The mixture of annual and quarterly data would not influence my selection of firm vs firm-time for clustering. I would do it the same way whether it were all annual, all quarterly, or a mix of the two.

The choice of what to cluster on is complicated and depends on the dependencies in the data. A good answer to firm vs firm-time would depends on a good understanding of the variables themselves. As you are apparently working in economics or finance, neither of which is my field, I don't have the necessary expertise to advise you on this aspect of it. There are many economists/econometricians who post on Statalist, and you would be better advised to repost this separately to get an answer from one of them.

Or, since you say you were already given advice on this in another post, look at who gave you the answer and find out what field they work in. If you click on their name, you can see their profile which, in the case of people who respond frequently, usually contains that information. If not, you can try Googling the person. Actually, you can also just carefully re-read the advice you were given to understand whether it makes sense and is consistent with the general guidance about these issues in your field. If they did not explain their opinion and just give you advice, you can post back on that thread and ask them to explain why they said what they said.