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  • Time-Invariant Variables in System GMM?

    Hi,

    In (Abdallah, Goergen and O'Sullivan, 2015), the authors mention that it is possible to include time-invariant binary variable in system GMM. Attached is the screenshot of the same. I would like to know if this is true. I think that time-invariant variables should get removed from the model as system GMM first differences the variables.

    References:

    Abdallah, W., Goergen, M. and O'Sullivan, N. (2015). Endogeneity: How Failure to Correct for it can Cause Wrong Inferences and Some Remedies. British Journal of Management, 26(4), pp.791-804.

    Attached Files

  • #2
    The conventional system GMM estimator uses instruments for a first-differenced version of the model, which obviously removes the time-invariant variables, and instruments for the level version of the model from which the time-invariant variables are not removed. Obviously, you still need to find appropriate instruments for these time-invariant regressors, an issue that appears to be often ignored when people make such statements as in your cited paper.

    You can find more elaborate answers to your question and potential follow-up questions in the following paper:
    • Kripfganz, S. and C. Schwarz (2015). Estimation of Linear Dynamic Panel Data Models with Time-Invariant Regressors. ECB Working Paper 1838, European Central Bank.
    https://twitter.com/Kripfganz

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    • #3
      Thanks a lot Sir. I went through your paper.

      1. I would like to know how should one go about estimating time-invariant regressors in STATA in a dynamic panel setting. Do regular commands like xtdpdsys offer us this option?
      2. If the concerned time invariant variable is not our variable of interest, can we simply proceed by ignoring it?
      3. FEM controls for all time-invariant variables together via within-group transformation. Hence, we do not perform any additional treatment to control them. I would like to know if system GMM is also controlling for all time-invariant variables together (like FEM) or not. If it is not controlling for all time-invariant variables, how can we make sure it does?

      Thanks!

      Comment


      • #4
        1. If you want to estimate the coefficients of time-invariant regressors, commands like xtdpdsys, xtabond2, xtdpdgmm allow you to specify those variables in the list of independent variables. You still need to specify appropriate instruments. For example, you could assume that those time-invariant regressors are uncorrelated with the "fixed effects". In that case, you also need to specify those variables as standard instruments for the level model. How to choose these instruments is not primarily an econometric problem. Your economic theory should guide you in this regard.
        2. If those variables are not of interest, you do not need to specify them and they become part of the unobserved "fixed effects". If all of your instruments are uncorrelated with any time-invariant variable, there is nothing you need to do.
        3. See my answer to the previous two questions. You need to choose instruments that are uncorrelated to any time-invariant variable if you do not include the time-invariant regressors as control variables. If you do include them, you need to specify instruments for those time-invariant variables. All other instruments still need to be uncorrelated with the remaining unobserved time-invariant effects.
        https://twitter.com/Kripfganz

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        • #5
          That's a very helpful response, Sebastian Kripfganz. Now, since time-invariant variables are not of my interest, I choose not to specify them in my model. However, with reference to your point #2, how do I statistically check whether instruments in my model (which are selected by the software itself by using lags of level and first-differenced variables) are not correlated with any time-invariant variable? I ask this specifically because time-invariant variables do not change over time by definition. Then, do we check their correlation with instruments across cross-sections?

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          • #6
            In the first place, this is an assumption that you need to justify. After the estimation, you can use the Hansen or Difference-in-Hansen test to check the validity of the overidentifying restrictions (loosely speaking: the instruments).
            https://twitter.com/Kripfganz

            Comment


            • #7
              Thanks a lot, Sir!!

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