I have a question regarding weighing observations by importance.
Suppose I am running the following regression:$$log(y_{it}/y_{it-1})=\alpha+\sum_{i=1}^{N}\gamma_{i}Country_{i}+u_{i}$$ where basically my LHS is GDP growth of country $i$ at time $t$ that I regress on a full set of country dummies (-1).
I want to weigh the observations by the GDP of the country.
If I am doing this on stata, what weights are appropriate? Frequency weights or probability weights? My intuition is that I have to basically run a weighted least squares regression of the form: $$ \hat{\beta}=(x'Wx)^{-1}(x'Wy)$$
where $W$ is a diagonal matrix with the weights (GDP) on the diagonal. I am at a loss regarding how to implement this on Stata. Thanks!