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  • #16
    Although it is unknown which critical values should be used for the ECT(-1) coefficient, the coefficients of y(-1) and ECT(-1) are equal, while both measure the same thing (i.e., the opposite of the speed of convergence). Based on that, I think that the statistical significance of ECT(-1) could indirectly be checked through the bounds t-test. Might this be a good workaround solution, thus making the bounds t-test absolutely mandatory in both the one- and the two-step approach?
    Last edited by John Costopoulos; 24 Jan 2022, 10:23.

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    • #17
      The coefficient estimate of y(-1) in the one-step EC model and the coefficient estimate of ECT(-1) in the two-step model are generally not equal; see for example the EViews output in Dave Giles' blog.
      https://twitter.com/Kripfganz

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      • #18
        Dear Sebastian,

        I would like to clarify that when I speak about a two-step approach I refer to the following case only:
        Step 1: Compute the ECT using either the long-run coefficients extracted (and subsequently normalized) from the unrestricted ECM or the long-run coefficients extracted from the corresponding ARDL model (e.g., Kripfanz and Schneider, 2018, slide 5).
        Step 2: Estimate a restricted ECM to find the short-run coefficients and the ECT(-1) coefficient.

        In contrast, Giles has extracted the long-run coefficients from an equation in levels (Eq. 5) in the first sub-step of his step 7. If his variables were not I(1), he would not be able to follow the approach described in Step 7.

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        • #19
          Now I see what you mean. In this case, the coefficients should indeed coincide and the bounds test will be applicable to the t-statistic from your two-step procedure.
          https://twitter.com/Kripfganz

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          • #20
            Dear Sebastian,

            Many thanks again. Everything is absolutely clear to me now! Unfortunately, the role of the bounds t-test is too underestimated in the empirical literature.

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            • #21
              John Costopoulos
              I had another look at this issue and need to revise my previous conclusion. If it is not known that all long-run forcing variables are I(1), then the error correction model should not be estimated in the two steps you proposed. The reason is that the standard errors in your second step would ignore the uncertainty regarding the estimation of the long-run coefficients. This will also affect the bounds test. See footnote 34 in Pesaran, Shin, and Smith (2001).
              https://twitter.com/Kripfganz

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              • #22
                Dear Sebastian,

                Thank you very much for your extremely helpful clarification. It was very kind of you to spend so much time with my questions.

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                • #23
                  how to interpret when ECT can not be Reject null Ho? (e.g coefficient of ECT is -0.19 but P-value is 0.122)

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                  • #24
                    how to interpret when ECT can not be Rejected null Ho? (e.g coefficient of ECT is -0.19 but P-value is 0.122)

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                    • #25
                      If the speed-of-adjustment coefficient is not statistically significantly different from 0, as indicated by a non-rejection of the t-statistic version of the bounds test, then no error correction / cointegration / long-run relationship exists. You can still interpret the short-run effects, but not the long-run effects.
                      https://twitter.com/Kripfganz

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                      • #26
                        Thank prof,
                        I have one more question below

                        Can I ignore some of the Diagnostic test such as heteroskedasticity or Ramsey Reset Test in ARDL-EC representation ?

                        e.g in my analysis, Serial correlation is ok, but some of my heteroskedasticity or Ramsey Reset Test is not ok, can ignore them?

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                        • #27
                          I have to note reference in my paper. Excuse me, Can you give me the reference of this solution below?

                          (If the speed-of-adjustment coefficient is not statistically significantly different from 0, as indicated by a non-rejection of the t-statistic version of the bounds test, then no error correction / cointegration / long-run relationship exists. You can still interpret the short-run effects, but not the long-run effects.)

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                          • #28
                            https://twitter.com/Kripfganz

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