‘What is the use of testing, say, the significance of regression coefficients, when maybe, the whole assumption of the linear regression equation is wrong?’ This is just the type of arguments we have discussed.

Without some idea of the power of statistical tests against interesting alternative hypotheses and/or some metric for evaluating the extent to which the data are inconsistent with a maintained hypothesis formal statistical tests are uninformative.

Science proceeds by falsifying theories and constructing better ones. Falsifications of hypotheses based on overidentifying restrictions … are unenlightening in two senses. First, they provide little insight into whether the reason for the theory’s failure is central to its logical structure or is instead a consequence of auxiliary assumptions made in testing it. … While in principle it would be possible to explore a range of possible assumptions, this type of ‘data mining’ is usually condemned by those who favor formal approaches to empirical work.

[S]ome of the methodological problems that contribute to the mountains of untrustworthy evidence could have been avoided if only textbook econometrics paid a bit more attention to some of the key methodological ideas in Haavelmo [1944].