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  • FGLS for heteroskedasticity (WLS) with weights

    Hi, a question more of process than actually having a problem.

    So consider that we want to use the FGLS estimator to model heteroskedasticity. As Cameron and Trivedi (2010) show this can be done with weighted least squares using aweight. The process is normally the following: estimate the homoskedastic model, predict the residuals, square the predictions, estimate the variance model using the squared of the predictions as the dependent variable, predict the variance, and use 1/variance prediction for aweight. So far so good.

    I was wondering... what happens if we want to use weights in our estimation? For example, we may be using survey data that provides weights and we want to use them in our estimation. If we do all the intermediate estimations using the weights, do we need to also include the survey weights in addition of weighting to do FGLS? If so, how? I was kind of thinking that since the intermediate steps have been using the survey weights, the prediction of the variance is affected by the survey weights, and thus we may not need accommodate for the survey weights in the final estimation.

    Help and thoughts would be appreciated, thanks!

    Reference:
    Cameron, A. Colin and Pravin K. Trivedi. 2010. Microeconometrics Using Stata. Revised ed. College Station, TX USA: Stata Press.
    Last edited by Alfonso Sánchez-Peñalver; 24 Nov 2015, 16:50. Reason: added the reference
    Alfonso Sanchez-Penalver

  • #2
    Hi Alfonso,

    I have come to the point in my modeling were this is an issue. I am in the exact situation you describe: trying to use FGLS estimator with complex survey data. Stata's svy command does not allow for aweights to be used. Were you able to get an answer or any thoughts regarding this issue?

    Many thanks!

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    • #3
      Hola Carlos,

      unfortunately no-one responded to this post and I didn't look for an answer anywhere else. Sorry that I can't be of any help. Thinking quickly, an alternative would be a maximum likelihood estimation where you model the heteroskedasticity in the equation for the variance/standard deviation. I know you can use svy with maximum likelihood. You would have to be content with having a maximum likehood estimation instead of a FGLS estimation. If you haven't looked at maximum likelihood programming in Stata, buy Gould, Pitblado, and Poi (2010). It's a very easy read with great examples. I know that this is giving you more work and not what you were looking for, but at least it's a workaround.

      Reference:
      Gould, William, Pitblado, Jeffrey, and Brian Poi. 2010. Maximum Likelihood Estimation with Stata. 4th. ed. College Station, TX: Stata Press.
      Alfonso Sanchez-Penalver

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      • #4
        Alfonso,

        Thank you so much for getting back to me and giving me more options. I had not come across Gould, Pitblado, and Poi(2010), I will give the book a look since it is in my university library. I have, however, been basing some of my models on Western, Bruce, and Deidre Bloom (2009)'s VFR; they compare ML with REML and Bayesian estimators and don't find significant differences in variance estimation with large samples. I will read the book you suggested to make sure I use the svy correctly with the ML. Thanks again for your advice, it helps me more than you can imagine! Gracias!

        Reference:
        Western, Bruce and Deirdre Bloome. 2009. Variance function regressions for studying inequality. Working paper, Department of Sociology, Harvard University.

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