how can I handle the influence of one country's observations on overall regression results? Currently I am working on one paper. I have 280 observations and 8 countries in my data set. I have run OLS regression model and all the results seem good. However, I am not convinced by the result of one of the variables and suspected one of the countries for possible influence. then I did run one regression for the whole sample and another regression for without that country. As expected I found the variable to be significant for the whole sample but not for the without x country. I am wondering how could I handle this problem?  
 A: You probably need to use a mixed effects model with "country" as a random effect.  It sounds like your interested in a question where multiple data points have been collected from these 8 countries, but the identity of the country is not what you are actually interested in.  You could model this in R with the lmer function in the lme4 package, or with PROC MIXED in SAS.
In R your model would probably look like
lmer(response ~ your predictors + (1|country),data = data)

If data from a single country is driving the significance of your results in a linear regression model, a mixed model should remove that effect.  Note that with 8 countries, you'd be at the minimum number of levels to the random effect.  You could make your results more robust in general by acquiring data from more countries.
A: I would run your regression and add an interaction between x and country if you have enough data. In Stata, that would be something like this (assuming your x is continuous):
reg y c.x##i.country, robust

The interactions allow the effect of x to vary by country. You can also add over covariates to the model.
However, if you are interested in the effect of a country-level variable that is constant within each country, it probably makes sense to cluster your standard errors at the country level to avoid running into the Moulton problem. Unfortunately, with only 8 countries you might have a problem since that is very few and this only works as the number of clusters goes to infinity. This also makes your SEs blow up most of the time. So you are between rock and a hard place.
There are also some subtleties about what you are trying to do and SEs. Is it to say something descriptive about y and x in the population of firms from these 8 countries, only some of which are sampled in your data? In that case, maybe areg, vce(cluster country) is better. Or do you want to extrapolate to firms from countries that you don't observe? Or are you trying to say something about your particular firms at another time (say if these 280 firms are not a sample or a census)?
