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  • panel data with cross sectional dependence and autocorrelation

    I have a panel data with N>T (N=157, T=15). Have taken log of a few variables to make it Heteroscedasticity free. for cross sectional dependence have used 'xtcdf' , for autocorrelation postestimation command 'hettest'. have a few questions. Please feel free to ask more questions about the data or its analysis. My questions are -

    1. For N>T micro data should cross sectional dependence be taken into account and controlled.
    2. Is there a thumb rule for taking the log of variable. Which ones to use and reject.
    3. Also if i dont take the logs, there is a presence of cross sectional dependence, autocorrelation and heteroscedasticity. Can we use xtscc, if yes how to chose between random/fixed effects. Mundlak is the way out?
    4. if none of the above options are correct, please suggest a way forward.

    hoping to hear from the community soon.

    Harsh

  • #2
    Harsh:
    welcome to this forum.
    1) -estat hettest- tests heteroskedasticity after -regress-, whereas it is not supported by -xtreg-;
    2) if you actually have a N>T panel dataset with heteroskedasticity, and systematic error correlated within and across panels, you should use the community-contributed module -xtscc- (with the caveat that theestimator is based on large T asymptotics);
    3) unfortuntely, neither -hausman-, nor the community-contributed module -xtoverid- allow comparing -fe- vs -re- specification with -xtscc-.
    Kind regards,
    Carlo
    (Stata 18.0 SE)

    Comment


    • #3
      Hi Carlo

      thanks for your prompt response. I have a few follow-up questions.

      1) for heteroskedasticity after xtreg i have used xttest3 command and got a p-value lower than 0.05. Thus heteroskedasticity is present.
      2) can T=15 (15 financial years) considered large T asymptotics.
      3) Hausman was ruled out as the data was heteroskedastic. Tried running Mundlak using The Stata Blog ยป Fixed effects or random effects: The Mundlak approach as a reference. It does give results not entirely sure if they are correct or can Mundlak be used entirely.
      4) Also could you shed some light if time fixed effects should be added to the regression model.
      5) any comment on taking the log of variables. I am using a number of ratios like tobinsq,roa, debt ratio among others.

      Hope to hear from you soon.

      Regards
      Harsh
      Last edited by Harsh Tuli; 21 Oct 2021, 04:25.

      Comment


      • #4
        Harsh:
        1) if you used -xttest3- (and wisely so) your previous command was -xtreg,fe-;
        2) not really, but -xtscc- can make it;
        3) as per its -help file-, -mundlak -
        estimates random-effects regressions adding group-means of independent variables to the model
        . It is an interesting approach when you should go -fe- but you're also interested in estimating the coefficients of time-invariant variables. Be sure that this is what you want. That said, -mundlak do not deal with autocorrelation across panels, as far as I know;
        4) in some instances, logging can reduce heteroskedasticity. Depending on what you logged, the interpretation of regression coefficients differ.

        Kind regards,
        Carlo
        (Stata 18.0 SE)

        Comment


        • #5
          Carlo
          1) yes my command before xttest3 was xtreg,fe.
          2) so If I understand everything Properly I should directly go for xtscc. And since mundlak isn't the right approach. How do I decide if I should use fixed/random? Do I need to do this...or is fixed the way to go?
          3) and if I do run fixed do I add time fixed effects. As the command testparm suggested additions of time fixed effects but they end up spoiling my results. Please suggest.

          Thanks Carlo for helping me out with this

          Regards
          Harsh

          Comment


          • #6
            Hi Harsh,

            Carlo provided excellent advice. If I were you, I would report Mundlak test results as they are the closest feasible and robust approximation of the test you can get.

            Subsequently, the Mundlak test will probably indicate that the unobserved heterogeneity is correlated with the regressors, and rule in favour of the fixed-effects model.

            Also, I don't know what field you're in, but in economics we tend to always include time FE and we very rarely go for random effects models as we pretty much always select within estimation for internal validity purposes. Even if time FE mess up your results, then I would try changing the specification, but always include time FE as a baseline rule.

            I would also strongly advocate the use of Driscoll Kraay standard errors as recommended by Carlo. What's more, these standard errors are robust to non-normally distributed residuals (you can test this using xtsktest by Alejo et al., 2013).

            Comment


            • #7
              Thanks maxence

              You are right mundluk did give fixed effects the preference in almost all cases baring the one where both random and fixed models were insignificant.

              How can I try changing my specifications? If fixed time effects mess up my results? Also I didn't write here but I did run the normality analysis and find out that the data was non normal using the test for Shapiro Wilk estimates.

              Could you suggest that if results are improving should u take log of variables. I did it on the basis that they should not be dummy variables or negative. What is your say on this? Is it the right way to go.

              In one of the forums I also read that if t is less than 20 we don't need to check or control cross dependence. Is that the case?

              Look forward to hearing from you.

              Regards Harsh

              Comment


              • #8
                I have another question -

                That if logging removes the heteroskedasticity...... What would be my course of action? Will I still go for xtscc or some other way.

                Harsh

                Comment


                • #9
                  What I meant concerning time FE is that there should always be time FE in a longitudinal regression, unless you are trying a robustness check. If you are not getting the results you want, try omitting / including different explanatory variables.

                  Personally, I would always test for CSD and the normal distribution of residuals.

                  As Carlo mentioned, logging a variable changes the coefficient's interpretation and may mitigate heteroscedasticity and autocorrelation, but not necessarily. I generally only tend to log variables whose level values are immense (e.g. GDP in USD).

                  If you data are in level form, perhaps compute the growth rate? (which you can also do through logarithms given their mathematical properties).

                  Best!
                  Maxence

                  Comment


                  • #10
                    Thanks alot Carlo and Maxence for clearing my doubts...I'll be using xtscc...!!!

                    Comment


                    • #11
                      Carlo and Maxence

                      What is the interpretation of the fixed time effects being significant. I've tried to find it across the forums but to no avail. Could you please help with that?

                      Regards
                      Harsh

                      Comment


                      • #12
                        Harsh:
                        when adjusted for the other predictors, -i.time- has a role in explaining within-panel variations of the regressand.
                        Kind regards,
                        Carlo
                        (Stata 18.0 SE)

                        Comment


                        • #13
                          Carlo i understand that it explains the variation but if we are writing the interpretation do we just mention that the time fixed effect explains the within panel variation or in some other way?
                          Also if i do end up taking logs of my variable which improves the results of the regression, how do we handle such logged variables in the case of interactions (in case of moderation objectives).

                          Thanks Carlo for being patient and answering all the queries.

                          Regards
                          Harsh

                          Comment


                          • #14
                            Harsh:
                            1) as yuou you're dealing with (I guess) a multiple regression (ie, with >1 predictor in the right-hand side of your regression equation) -i.time- works adjusted for theother ones. Hence, when adjusted for the other predictors, -i.time- has a role in explaining within-panel variations of the regressand.
                            -testparm- tests the joint statistical siginificance of all the years (less the reference category: that is, n-1) of the categorical variable -year-. This detail shuold be reported in the methodological section of your paper/research report/else.
                            2) you neither provided an example, nor tell potentially interested listers what you logged and where (left-hand side? right one? both).
                            Kind regards,
                            Carlo
                            (Stata 18.0 SE)

                            Comment


                            • #15
                              Carlo I logged my variables both right and left sides. For example left side variable performance and right side variable diversification. Even the control variables have been logged. But I don't really know what to do if I'm checking a moderating effect/interactions. Thus these questions. Is logging all variables legitimate?

                              Yes Carlo its a multiple regression for a few models.
                              Last edited by Harsh Tuli; 22 Oct 2021, 07:49.

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