I have unbalanced panel data where 2213 companies from 32 different countries report several measures annually between 2005 and 2019.

Here are several outputs from the baseline regression model (reg Y X1 X2 ControlVariables i.country i.time,r) as follows:


1 2 3 4 5 6
X1 -0.045 0.641 0.215 0.850
(-0.42) (7.23)*** (2.20)** (8.31)***
X2 -0.605 -0.459 -0.627 -0.560
(-8.43)*** (-8.27)*** (-9.06)*** (-9.03)***
Control Variables YES YES YES YES YES YES
Constant YES YES YES YES YES YES
Time Fixed Effects YES NO YES NO YES NO
Country Fixed Effects YES NO YES NO YES NO
N. of Obs. 24611 24611 24381 24381 24368 24368
F-stat 11.84 31.98 11.84 35.33 11.67 32.33
R² 0.1273 0.0932 0.1317 0.0939 0.1319 0.0973


Y is the observed riskiness whereas X1, X2, and control variables are different measures of a company in a year. I present t-statistics in parentheses under the 𝛽 coefficients and denote 1%, 5% and 10% significance levels with ***, ** and *, respectively.

My questions are more regression interpretation related rather than a specific Stata feature:

1-) How does the lack of time and country fixed effects alter the coefficient for X1 some much in model 2 (compared to model 1) but not for X2 in model 4 (compared to model 3)?
2-) How does adding X2 alter the coefficient for X1 some much in model 5 (compared to model 1)?
3-) How does the lack of time and country fixed effects alter the coefficient for X1 some much in model 6 (compared to model 5) but not for X2?
4-) Why do F-stat increase and R² decrease in the lack of time and country fixed effects (model 2 versus 1 and model 4 versus 3 and model 6 versus 5)?
5-) How do you describe the differences between the independent variables X1 and X2 given their different responses to the lack of time and country fixed effects concerning their explanatory power over Y? Would you agree that X2 works well on its own to explain Y but X1 suffers from omitted variable (X2) bias?

Please feel free to dismiss my questions above to make your own interpretation of the outputs. I appreciate it if you don't neglect question 5 though.

I also welcome Stata relevant recommendations (e.g., using xtreg or performing Hausman test etc.) for the sake of more robust interpretations.

Best,

Lütfi