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The robustness test failed, can we not let go?
Of course. It is best to do a robustness test after making a regression model, especially when doing a paper. Robustness test can make the selection of regression variables more rigorous (Ramsey test), make the structure of regression equation more stable (Zou test), and make the paper more convincing through robustness test. If robustness testing fails, it shows that it is not rigorous enough, so we can put it aside and make a new robustness testing and evaluation.