Time and country fixed effects as dummies change significance

[Marta Castro]

Dear Statalist,

I am doing a research about microfinance institutions and the factors that influence their performance (inflation, GDPpc, credit by commercial banks...). I have a dataset of 88 institutions in 6 countries (region of South Asia) and for the period 2011-2015. Since I have a short panel, I am including time fixed effects and year fixed effects as dummies as suggested by my professor.

Code:
reg performance indepvar1 indepvar2, robust
reg performance indepvar1 indepvar2 i.Country, robust
reg performance indepvar1 indepvar2 i.Year, robust
reg performance indepvar1 indepvar2 i.Country i.Year, robust

I would like to know hot to interpret the results if, for example, inflation was significant in the first regression, not significant in the second and third regressions and significant again in the last regression including both dummies. Or, if credit by banks was significant in the first two regressions but not in the last two regressions. Any suggestions on how could I interpret my results?

Thank you very much!

[Clyde Schechter]

These are all different models and there is nothing unusual or surprising about the coefficient of a variable changing when other covariates are added or removed from the model. The changes can be large, even opposite in sign (let alone something as unimportant as change in significance). This phenomenon is sometimes referred to as Simpson's paradox. Wikipedia has a good explanation of it in the context of contingency tables of categorical variables, but the principles underlying it are exactly the same. The question is which of these models is (are) the appropriate ones to answer your research question(s). That is a substantive question, not a statistical one nor one that pertains to Stata specifically. Probably the best resource for this is to confer again with your professor, especially since he or she suggested these in the first place.

[Carlo Lazzaro]

Marta:
as an aside to Clyde's excellent advice, I wonder why you do not go -xtreg- with a panel data structure.
Eventually, if institutions are nested within countries, you may also consider -mixed-.