# Econometrics: Weights in regression that contains averages

Let's say I have a regression of the form:

$$y_j=a_0+a_1*T_j+a_2*X_j+u_j$$

where $j$ stands for county, and $y$ and $X$ are averages over worker outcomes/characteristics for each county, and $T$ is a continuous treatment variable that varies at county level.

When estimating in Stata I was suggested to use "aweight" option, where analytical weights are derived from county population.

Question:

Now I want to include county population as a control variable. Wouldn't this cause a problem as I am already using county population for weights?

Thanks!

• If I understood well your first question, you could use and interaction term as "country population * treatement variable". This will be another variable with another elasticity term, let's say $a3$. So, after you could look if it interfers. You can look at the AER paper Burnside and Dollar (2000), all the methodology is well explained. Aug 10 '15 at 18:54
• @optimalcontrol Thanks you for the reference, I will take a look! Also, I've just simplified the question a bit to get to the essence.. Aug 10 '15 at 19:03
• aweights are typically used when observations represent averages and the weights are the number of elements that gave rise to the average. Unless your averages are calculated for the whole population of the county (rather than some subset), you may have a problem (depending on what derived means). Nov 5 '15 at 0:48
• @DimitriyV.Masterov thanks for comment! I see it now. Nov 11 '15 at 22:07