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I have a question about a time invariant variable in a panel data model.

As we know, we can estimate the coefficient of a time invariant regressor using pooled ordinary least squares (OLS) or a random effects model (a kind of pooled feasible generalized least squares [FGLS] model). But suppose we are interested in the coefficient of a "time-invariant" regressor. Why do we have to use a panel data model? What is the advantage of using a pooled model rather than a cross-sectional model except sample size?

Thank you for your time spent reading this question.

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But suppose we are interested in the coefficient of a "time-invariant" regressor. Why do we have to use a panel data model?

You don't have to. In general, if you observe a cross-section of entities at multiple points in time, why not use a panel data model? Why throw out the longitudinal variation?

What is the advantage of using a pooled model rather than a cross-sectional model except sample size?

You correctly note that with more degrees of freedom and more sample variability you improve inference. Estimates should be more efficient using panel data. In particular, a panel of individuals will help you understand more complex human behavior than using a sampling of persons at one point in time. A paper by Cheng Hsiao highlights many useful advantages of panel data. I reproduced below some of the principal advantages:

  1. Constructing and testing more complicated behavioral hypotheses
  2. Evaluating the effectiveness of social programs
  3. Controlling the impact of omitted variables
  4. Uncovering dynamic relationships
  5. Generating more accurate predictions for individual outcomes
  6. Providing micro foundations for aggregate data analysis

The paper is ungated so please peruse it at your leisure. Another type of model that should interest you is the between-effects model, which 'averages out' the longitudinal dimension. Simply average the data over time $t$ for each $i$ unit and then regress the averaged variables on each other.

To conclude, I can't offer any hard-and-fast rules to help you choose a model as your question is already very broad. I do recommend exploiting any time variation present in your data. If estimates associated with your time invariant regressors are of substantive interest, then random effects is a safe choice.

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  • $\begingroup$ your answer is very informative for me. Because I am not good at English, I cannot express my appreciation perfectly. But, I want you to know that I really thank you. $\endgroup$
    – M.C. Park
    Dec 18, 2020 at 7:18

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