WLS estimation in Stata

[Karen Arulsamy]

Hi there,
When employing WLS, one approach is to divide the main equation model by 1/sqrt(X).
However, when estimating this in Stata, one would weight the equation by 1/X as follows:

Could someone explain to me why this is the case?

Is it because we are minimizing the weighted sum of squared residuals with respect to 1/X? However, theoretically, we divide each component in the main equation by 1/sqrt(X)?

clear all
bcuse saving
reg sav inc size educ age black
gen w1 = 1/inc
reg sav inc size educ age black [aw=w1]

Thank you in advance for your help with this.

Many thanks
Karen

[Jeff Wooldridge]

When you specify aweights in Stata you use the inverse of the variance. It’s the squared residual that is weighted.