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This question might sound very silly, but I haven't found a clear answer so far.

Suppose you are working with a panel including several time series data for different countries/cities/firms: when analyzing the panel in a regression is it somehow mandatory to consider time and countries/cities/firms fixed effects? If this is not the case, what makes you decide when these have to be considered or not?

Thanks

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  • $\begingroup$ There is a discussion of different ways to specify time in panel data models here ... stats.stackexchange.com/questions/323549/… Also, Singer and Willett's book Applied Longitudinal Data Analysis has one of the best discussions I'm aware of in the literature about a range of specifications of time in order to tease out different relationships. P. 210 in their book discusses Mosteller and Tukey's suggestion of a 'ladder of transformations and the rule of the bulge.' Could be useful. $\endgroup$ – Mike Hunter Jan 24 '18 at 12:19
  • $\begingroup$ Hi @DJohnson, it is certainly a good discussion, but here I am not talking about time series forecasting or dimensionality reduction or transformation. What I am talking about here is something way less elaborated: something like this dartmouth.edu/~ethang/Lectures/Class17/… . Now I know that generally in panel regression, you want to control for time and country fixed effect, I was just wondering if this is always the case or if there is a rule that you can apply to decide if the control should be used or not $\endgroup$ – Nemesi Jan 25 '18 at 14:05
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    $\begingroup$ For the most part it is always the case to control for cross section and temporal variance, esp since these are the key structural factors in the data. In fact, I'm not aware of anything in the PDM literature where this is not done. $\endgroup$ – Mike Hunter Jan 25 '18 at 21:40
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Please, consider that this is not THE way to go, it is just a quick roadmap to start analyzing panel data. A more rigorous procedure should be tested for the specific case of the user and supported by the literature.

After studying a bit more in detail the topic, although there is not a standardized procedure to apply to these analyses, a sequential approach that could be adopted is the following (ref and more info in this website and this video):

(example code in R using the plm package)

  • clean the panel data and set up the panel analysis (not explained here);
  • Estimate a simple OLS model

    OLS<-plm(Y ~ X, data = my_panel, model = "pooling")
    
  • Estimate a random effect model

    random<-plm(Y ~ X, data = my_panel, model = "random")
    
  • Estimate a fixed effect model

    fixed<-plm(Y ~ X, data = my_panel, model = "within")
    
  • Test the difference between the models

    # LM test for random effects versus OLS
    plmtest(OLS)
    

if the p-values is small enough, it will indicate alternative hypothesis: significant effects, then opt for a random effect model.

    # LM test for fixed effects versus OLS
    pFtest(fixed, OLS)

if the p-values is small enough, it will indicate alternative hypothesis: significant effects, then opt for a fixed effect model.

    # Hausman test for fixed versus random effects model
     phtest(random, fixed)

if the test suggests alternative hypothesis: one model is inconsistent, then it would be more appropriate to go for a fixed effect model.

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