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I am estimating a model y=b0 +b1*se+b2x +e where y are estimated coefficients from other regressions and se their respective standard errors. x is an exogeneous independent variable. My question is now, if I have to use weighted least squares in this situation as the heteroskedasticity caused by the fact that y are estimates with different variances is already accounted for by including the standrad errors as independent variable.
What is the difference of dividing everything by the standrd error and then applying OLS (i.e. WLS) or accounting for the bias by adding b1*se to the model?

Thanks
Slodge

I am estimating a model y=b0 +b1*se+b2x +e where y are estimated coefficients from other regressions and se their respective standard errors. x is an exogeneous independent variable. My question is now, if I have to use weighted least squares in this situation as the heteroskedasticity caused by the fact that y are estimates with different variances is already accounted for by including the standrad errors as independent variable.
What is the difference of dividing everything by the standrd error and then applying OLS (i.e. WLS) or accounting for the bias by adding b1*se to the model?

Thanks
Slodge

Adding se to the regression might account for bias in the mean of the coefficient b2, although it isn't obvious why there should be any bias. Doing WLS corrects for the standard error of b2 and improves the efficiency of the estimation.