My data is a panel of countries by year. Suppose my main RHS variable is a country's GDP and my main LHS variable classifies countries by whether the country is a democracy.
Is it desirably to weight each observation by the country's population in a particular year? Since the world population has generally increased over time, does that put too much weight on more recent time periods? To account for that, should I instead weight each country's population by say its population in the initial for each of that country's observations?
Also, isn't one purpose of weighting to correct for heteroskedasticity? Should I still adjust standard errors by using robust standard errors? Or, does using robust standard errors obviate the need to weight?
Should the weighted and unweighted regressions yield similar results?