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  • Breusch Pagan vs. White test for heteroskedasticity

    Dear all,

    When I tested for heteroskedasticity, the Breusch Pagan gave a contradicting result to the White test. And my question is: which test should I trust?

    I know the White test tests for nonlinear forms of heteroskedasticity. Does that mean that I have a nonlinear heteroskedasticity that was not picked up by Bresuch-Pagan test?


    My regression is of the following form: Y x1 x2 x3 x4^2 x6 x6 x7 x8 x9

    Here is my output:

    [Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
    Ho: Constant variance
    Variables: fitted values of y

    chi2(1) = 0.66
    Prob > chi2 = 0.4164

    . imtest, white

    White's test for Ho: homoskedasticity
    against Ha: unrestricted heteroskedasticity

    chi2(51) = 104.38
    Prob > chi2 = 0.0000

    Cameron & Trivedi's decomposition of IM-test


    Source chi2 df p

    Heteroskedasticity 104.38 51 0.0000
    Skewness ```````````````34.16 9 0.0001
    Kurtosis 31.13 1 0.0000

    Total 169.67 61 0.0000]
    Last edited by Maya Lani; 24 Apr 2017, 04:40.

  • #2
    Dear Maya Lani,

    How many observations do you have?

    Best wishes,

    Joao

    Comment


    • #3
      Different tests are discussed on pp. 3-6 of

      http://www3.nd.edu/~rwilliam/stats2/l25.pdf

      Key excerpts:

      The default Breusch-Pagan test specified by hettest is a test for linear forms of heteroskedasticity, e.g. as y-hat goes up, the error variances go up. In this default form, the test does not work well for non-linear forms of heteroskedasticity, such as the hourglass shape we saw before (where error variances got larger as X got more extreme in either direction). The default test also has problems when the errors are not normally distributed.White’s general test for heteroskedasticity (which is actually a special case of Breusch-Pagan) can be used for such cases.
      -------------------------------------------
      Richard Williams, Notre Dame Dept of Sociology
      Stata Version: 16.1MP (2 processor)

      EMAIL: rwilliam@ND.Edu
      WWW: https://www3.nd.edu/~rwilliam

      Comment


      • #4
        Dear Joao Santos Silva I have 1115 observations

        Comment


        • #5
          Dear Maya Lani,

          Thank you for the information. With that sample size it may be acceptable to use the White test. However, the test has a large number of degrees of freedom and it tends to over-reject in that case. On the other hand, as Richard Williams noted, the version of the BP test implemented by Stata will have little power against common forms of heteroskedasticity.

          My recommendation would be to follow the advice in Jeff Wooldridge's book and use the BP test including both the fitted values and their squares. This is an approximation to White's test but only has 2 degrees of freedom. Of course, you should use the version of the test that is robust to non-normality (that is, use the options iid or fstat).

          Best wishes,

          Joao

          Comment


          • #6
            Dear Joao Santos Silva thank you very much for the clear answer. I shall follow your advice

            Comment


            • #7
              Hi Maya,

              A different approach often used in economics is not to worry about testing and just use hetero robust standard errors. If there is no important hetero then these standard errors will not be much different from OLS standard errors, if there is hetero then robust standard errors will capture that. If you test first and then decide on the relevant estimator (hetero or no hetero) after, then that is called pre-testing and there is some evidence to suggest that the pre-test estimator is not always best. In other words, just using robust standard errors in a general sense (without testing) might be a good approach.

              Cheers, Eddie

              Comment


              • #8
                One thing I note on p. 2 of the handout I linked to above is that what appears to be hetero may actually reflect specification problems. For example, it may be that the model needs to include interaction or squared terms. I recommend that people consider such possibilities before jumping to other solutions.
                -------------------------------------------
                Richard Williams, Notre Dame Dept of Sociology
                Stata Version: 16.1MP (2 processor)

                EMAIL: rwilliam@ND.Edu
                WWW: https://www3.nd.edu/~rwilliam

                Comment


                • #9
                  Eddie is right in writing that (health) economists often use robustified standard errors by default. However, in most papers/articles the issues raised by Richard (e.g. heteroskedsticity due to regression model misspecification) are usually left unreported, and the reader/reviewer should trust the authors about the correct specification of the regression model.
                  Hence, I would recommend to perform a thorough post estimation assessment before deciding to go -robust-.
                  Kind regards,
                  Carlo
                  (Stata 16.0 SE)

                  Comment


                  • #10
                    Dear All,

                    There are some very interesting comments in this thread, and I would like to add my two cents.

                    Originally posted by Eddie Oczkowski View Post
                    In other words, just using robust standard errors in a general sense (without testing) might be a good approach.
                    The hetero tests can be used for more than just the choice of variance estimator to use. Knowing whether or not there is heteroskedasticity may be interesting in itself (e.g., it is important if we need to do prediction). Also, the results of the tests also provide information on the degree of heteroskedasticity and that may also be interesting.

                    Originally posted by Richard Williams View Post
                    One thing I note on p. 2 of the handout I linked to above is that what appears to be hetero may actually reflect specification problems.
                    In economics, a key source of heteroskedasticity is heterogeneity, a bit like in the example that Richard provides, but that is not necessarily misspecification. It may be that the variable z in Richard’s example is unobservable (for example, individual tastes) or that we do not want to condition on it (suppose we want to see how education affects wages and z is a dummy for occupation).

                    Especially with individual data, heteroskedasticity is very much to be expected so a hetero test is more to provide information on its magnitude than to test for its presence. Also, because heteroskedasticity is to be expected, it is hard to read too much into it in terms of misspecification.

                    Originally posted by Richard Williams View Post
                    For example, it may be that the model needs to include interaction or squared terms. I recommend that people consider such possibilities before jumping to other solutions.
                    Originally posted by Carlo Lazzaro View Post
                    Hence, I would recommend to perform a thorough post estimation assessment before deciding to go -robust-.
                    I totally agree that it is often important to check for misspecification but in view of the results in this paper I would not rely on heteroskedasticity tests to provide information on misspecification. Personally, I am a great fan of the RESET, which is particularly well suited to detect the need to include interactions or squared terms.

                    Best wishes and apologies for the long post,

                    Joao



                    Comment


                    • #11
                      And I'll add my once cent. Like Joao, I'm leery of using tests for heteroskedasticity to say anything about the conditional mean. It's essentially impossible to use such a test to distinguish between conditional mean misspecification and nonconstant conditional variance. That's why in the early 1990s -- for example, Wooldridge (1991) -- I proposed first testing the conditional mean using heteroskedasticity-robust tests, and then testing the homoskedasticity (or other variance restriction) using a test robust to asymmetry and heterokurtosis. One of the lessons there is that using a test for heteroskedasticity to conclude something about the mean is not a good idea.

                      Like Joao said, if the goal is to test the functional form of the mean, RESET, make robust to heteroskedasticity, is a much preferred option.

                      Comment


                      • #12
                        I'm leery of using tests for heteroskedasticity to say anything about the conditional mean. It's essentially impossible to use such a test to distinguish between conditional mean misspecification and nonconstant conditional variance.
                        Just on the basis of a hetero test, I would not say the model is mis-specified. But I would consider the possibility that model mis-specification is affecting the hetero test, and then consider and examine further what that mis-specification might be. Mostly, I don't think people should run a hetero test and then immediately jump to robust standard errors or weighted least squares or whatever. An omitted interaction term might be the real culprit, as I point out on p. 2 of http://www3.nd.edu/~rwilliam/stats2/l25.pdf.
                        -------------------------------------------
                        Richard Williams, Notre Dame Dept of Sociology
                        Stata Version: 16.1MP (2 processor)

                        EMAIL: rwilliam@ND.Edu
                        WWW: https://www3.nd.edu/~rwilliam

                        Comment


                        • #13
                          I guess a different way to make my point is that one shouldn't get to the heteroskedasticity test before computing conditional mean diagnostics. Use RESET, test for interactions, test for power transformations, always using a heteroskasticity-robust test. If you pass these, you may not even care to test for hetero. But if you do, you can be fairly confident that a rejection largely picks up nonconstant variance. No doubt there are cases where a variance test can have higher power than a mean test for detecting conditional mean misspecification, but I have to believe those are rare.

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