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  • Using square term in system-GMM estimation

    Hello

    I am attempting to estimate a dynamic panel data model using System-GMM (two-step). In doing so, I have been reading David Roodman (2009) paper on " How to do xtabond2: An introduction to difference and system GMM in Stata" along with Baltagi (2005) book on panel data.

    My enquiry to the members is the following:

    I am estimating say, Y(it) = alpha + Beta(1) X + Beta(2) Z; of which both X and Z are both endogenous. However, I would also like to examine a square term of the variable X.

    But I am not sure whether one should incorporate a square term in the system-GMM estimation. This is because Roodman (2009) mentions that both Difference-GMM and System-GMM estimators are designed for a linear functional relationship?

    Can one consider a square term in such an estimation method?

    Many thanks,

    Sagnik

  • #2
    The linear relationship mentioned by Roodman refers to a "linear-in-parameters" relationship. Using squared terms of X still leaves the model linear in the parameters. You can treat the squared term just as any other regressor.
    https://twitter.com/Kripfganz

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    • #3
      Thank you, Prof. Kripfganz for your reply. However, this brings me a couple of question more:

      1. I believe interaction terms could also be utilized in the model specification; and

      2. For the instruments of the square term, does the instrument generated in the system-GMM method (i.e., lagged levels and lagged differences of the endogenous variables) are sufficient to solve the endogeneity problem?

      Many thanks,

      Sagnik


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      • #4
        1. Yes.

        2. As with any instrumental variable estimator, the GMM estimator requires that you have at least as many instruments as regressors. These instruments need to be sufficiently correlated with the regressors and uncorrelated with the error term. If you can argue that the lagged variables satisfy these conditions (based on theoretical thoughts and the usual specification checks), then the answer is yes.
        https://twitter.com/Kripfganz

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        • #5
          Thank you, Profesor.

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