Panel data estimation method for country analysis

[Vasco Graca]

I'm working on a paper for a class where I'm analyzing how inflation and domestic exchange rate strength impact demand for cryptocurrencies, and whether this varies depending on the country's level of economic development. I have a dataset of 12 countries over 70 months. This is what the model looks like at the moment:

The "ln" indicates the natural log of the variable and I've included interaction terms between the relevant regressors and level of development. Additionally, lnbtc controls for the price of bitcoin.

Now that the data is collected and the model is built (unless you see a fundamental flaw), I am struggling to determine which estimation method to use. The most logical option seems to be to use time-fixed effects (xtreg y x, fe) to help account for the time-variant omitted variables that I was unable to control for given the unavailability of data (e.g., general increase popularity and accessibility of crypto as a whole). However, I'm concerned that I'm completely missing something that would suggest I use random effects or clustered errors.

Sorry if this question is pretty open-ended, but I've read and re-read my textbook and haven't been able to come to a conclusion yet.

Thanks in advance!

Edit: Forgot to mention that when I run the regression, I include a dummy variable for months (i.month).

[Maxence Morlet]

Don't forget time fixed-effects, and given that T>N if I were you I would give the community-contributed command xtscc a try. I just saw you included that in the edit, great.

I do not know the specific field of your research very well, but does a linear-log model in your case make sense? Up to you to decide.

Although in your case T/N does not really tend to infinity, but at least you have 70 time periods.

You definitely have too few countries to cluster at the country level.

[Joro Kolev]

What Maxence says is a good start: You can use the user written -xtscc-, include country, and time period fixed effects; this would be a reasonable estimation method for your data.

Note that monthly fixed effects are different from period fixed effects.

[Vasco Graca]

Thank you both for the input! For the purpose of the paper, I managed to simplify the regression but I'll be including the xtscc command as part of my discussion.