Feasible Generalized Least Squares (FGLS) and Instrumental Variable approach

[Boris Xen Wil]

Hi,


I try to regress the following FE-model: y_i,t = b₀ + b_1*x1_i,t + b_2*x2_i,t + b_3*x3_i,t + yearFE + stateFE. Im interested in the effect of x1 (grants) on y (expenditures).
Due to heteroskedasticity coming from the different sizes of the states I want to apply a FGLS and give the observations different weights.

According to this video I do the following in STATA (https://www.youtube.com/watch?v=x7m3uhTGcbk):

xi: reg y x1 x2 x3 i.year i.state
predict uhat, resid

gen uhat2 = uhat^2
gen loguhat2 = ln(uhat2)

xi: reg loguhat2 x1 x2 x3 i.year i.state

predict ghat, xb

gen hhat = exp(ghat)

xi: reg y x1 x2 x3 i.year i.state [aweight = 1/hhat]


The last regression acutally gives me the results which are predicted by the model. I also want to apply an instrumental variable approach where I instrument x1 by z. Does anyone know how to implement this in STATA respectively could somone recommend me any literature regarding FGLS and IV?

Thanks!
boris

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. By the way, in recent versions of Stata, the xi: prefix is not needed.

Without saying I fully buy your analysis, xtivreg gives you instrumental variables. It works with robust standard errors. xtgls gives you a much more flexible approach to panel data error structures, but not instrumental variables. The eregress routines might also do what you want, but I'm not sure.

[Boris Xen Wil]

Thanks for your answer.
I have found another post where someone was looking for the same thing: (https://www.stata.com/statalist/arch.../msg00536.html). Unfortunately no answer since 2003...

In the meantime I have found another solution using the xtgls command as follows:

xi: xtgls y x1 x2 x3 i.year i.state, corr(independent)  panels(heteroskedastic)

Unfortunately this is still not the IV estimation but perhaps someone know how to adapt the xtgls command for IV estimation?

[Boris Xen Wil]

Phil, I have just seen one of your posts in 2011 (https://www.stata.com/statalist/arch.../msg00384.html). Seems like we have a similar problem. I have also observation which vary massively in size. That's why I would like to estimate a FGLS. How did you solve the problem?