Specification Problems and Empirical Study

Peter Kennedy wrote: Econometric textbooks are mainly devoted to the exposition of econometrics for estimation and inference in the context of a given model for the data-generating process. The more important problem of specification of this model is not given much attention, for three main reasons: (1) specification is not easy; (2) most of econometricians would agree that specification is an innovative/imaginative process that cannot be taught; (3) there is no accepted "best" way of going about finding a correct specification. (Of course, this is why we can always contribute something here, it is too hard to find a best and perfect way of specification.)

So the issue can come as how much trust do we have in econometrics, different people express in a different way:
All models are wrong, but some are useful. - George Box
Models are to be used, but not to be believed. -Theil, H.


Here is what Edward E. Leamer contributed into the discussion:
When an inference is suspected to depend crucially on a doubtful assumption, two kinds of actions can be taken to alleviate the consequent doubt about the inferences. Both require a list of alternative assumptions. The first approach is statistical estimation which uses the data to select from the list of alternative assumptions and then makes suitable adjustments to the inferences to allow for doubt about the assumptions. The second approach is a sensitivity analysis that uses the alternative assumptions one at a time, thereby demonstrating either that all the alternatives lead to essentially the asame inferences or that minor changes in the assumptions make major changes in the inferences. For example, a doubtful variable can simply be included in the equation (estimation), or two different equations can be estimated, one with and one without the doubtful variable (sensitivity analysis).
Simplification is a third. The intent of simplification is to find a simple model that works well for a class of decisions. A specification search can be used for simplification,as well as for estimation and sensitivity analysis. the very prevalent confusion among these three kinds of searches ought to be eliminated since the rules for a search and measures of its success will properly depend on its intent.

Again, Peter Kennedy gave following summarization: 
♣ Models whose residuals do not test as insignificantly different from white noise (random errors) should be initially viewed as containing a misspecification, not as needing a special estimation procedure.
♣ "Testing down" is more suitable than "Testing up"; one should begin with a general, unrestricted model and then systematically simplify it in light of the sample evidence.
♣ Tests of misspecification are better undertaken by testing simultaneously for several misspecifications rather than testing one-by-one for these misspcifications.