I am trying to expand my knowledge about the different interpretations of combinations of fixed effects.

I am using a dataset with observations at the firm level. The dataset spans multiple countries over 2 years (2010-2015).

My question is very simple. In this scenario, what is the difference of interpretation between including country and year fixed effects, or country-year fixed effects? Is it also possible to include both?

Is there a case to be made for each option when taking into account my dataset?

I read the following on another site:

# When you interact state and year dummies (i.e. when you include state, year, and state*year in the regression,
# which by the way is the same as creating state-year dummies and including them in the regression), you are
# assuming that the unobserved state-level heterogeneity varies over time. Also, you are assuming the time effect
# to vary by state. If you include state and year separately and no interaction, you are assuming that the unobserved
# state-level heterogeneity is constant over time.

If I read this, I get the feeling that it is always better to include the interactions. But in statistics, nothing seems to come for free. So what is the downside here?