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Shall we anticipate the regression result? Saying the coefficient sign .

  1. If not, why?
  2. If so, what should we do when it fails to achieve anticipated results?
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    $\begingroup$ youtube.com/watch?v=OL6-x0modwY $\endgroup$ – snoram Aug 28 '16 at 21:38
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    $\begingroup$ Many times the data tells you something you don't expect, and that is informative by itself. It could be a bad thing if it is measurement error, etc, or a good thing if you have theoretical insights why the unexpected result might be relevant. $\endgroup$ – luchonacho Aug 29 '16 at 9:57
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Saying what the theory predicts is a good idea as then we can make a testable hypothesis of the theory. Much of empirical economics is to test the validity of the theory.

If your result conflicts with the theory, then you can try to rectify the conflict or propose a better alternative.

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If you have prior beliefs, there are well-established ways to incorporate them into your analysis.

The traditional way is to reinterpret your analysis, or look for additional data to back up your prior beliefs. This is very poor science, but sadly it's incredibly common. So you'll always have the excuse of there being plenty of precedents in the literature. There are specific conditions required for linear regression to be valid, but most people using it, will never bother testing whether they apply before wading in. Don't be "most people".

The rigorous way, the scientific way, to do it is to incorporate your prior beliefs into your analysis from the beginning; so use something such as Bayesian regression.

As Andrew Gelman says:

when data are weak and there is strong prior information that is not being used, classical methods can give answers that are not just wrong — that’s no dealbreaker, it’s accepted in statistics that any method will occasionally give wrong answers — but clearly wrong, obviously wrong. Wrong not just conditional on the unknown parameter, but conditional on the data. Scientifically inappropriate conclusions.

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